Content-Type: multipart/mixed; boundary="-------------0410150125337" This is a multi-part message in MIME format. ---------------0410150125337 Content-Type: text/plain; name="04-324.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-324.comments" 9 pages, no figure ---------------0410150125337 Content-Type: text/plain; name="04-324.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-324.keywords" Navier-Stokes equation, vorticity, uniqueness, symmetric rearrangements ---------------0410150125337 Content-Type: application/postscript; name="dirac.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="dirac.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: dirac.dvi %%Pages: 9 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips dirac -o dirac.ps %DVIPSParameters: dpi=600, compressed 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Fp(is)f(a)g(con)m(tin)m(uous)h(function)e(if)g Fo(f)40 b Fp(is)29 b(con)m(tin)m(uous.)141 5551 y(W)-8 b(e)29 b(next)e(in)m(tro)s(duce)f(a)i(partial)e(order)h(on)g(in)m(tegrable)g (functions)f(whic)m(h)g(is)g(based)h(on)g(rearrangemen)m(ts.)1867 5800 y(5)p eop %%Page: 6 6 6 5 bop 0 91 a Fl(De\014nition)35 b(4.1)46 b Ff(L)-5 b(et)33 b Fo(f)5 b(;)15 b(g)28 b Fp(:)e Fl(R)1114 58 y Fn(N)1207 91 y Fm(!)f Fl(R)32 b Ff(b)-5 b(e)32 b(inte)-5 b(gr)g(able)33 b(functions.)42 b(We)32 b(say)g(that)i Fo(f)41 b Ff(is)32 b Fp(dominated)f Ff(by)h Fo(g)k Ff(if)956 209 y Fj(Z)1006 415 y Fn(B)1059 426 y Fe(R)1129 332 y Fo(f)1184 295 y Fk(#)1246 332 y Fp(\()p Fo(x)p Fp(\))15 b(d)p Fo(x)41 b Fm(\024)1638 209 y Fj(Z)1689 415 y Fn(B)1742 426 y Fe(R)1811 332 y Fo(g)1857 295 y Fk(#)1921 332 y Fp(\()p Fo(x)p Fp(\))15 b(d)p Fo(x)93 b Ff(for)33 b(al)5 b(l)34 b Fo(R)26 b(>)e Fp(0)33 b Fo(;)770 b Fp(\(4.1\))0 604 y Ff(wher)-5 b(e)34 b Fo(B)326 618 y Fn(R)409 604 y Fp(=)25 b Fm(f)p Fo(x)g Fm(2)g Fl(R)791 571 y Fn(N)874 604 y Fm(j)15 b(j)p Fo(x)p Fm(j)26 b Fo(<)f(R)q Fm(g)p Ff(.)42 b(In)33 b(this)g(c)-5 b(ase,)33 b(we)g(write)g Fo(f)h Fm(\026)25 b Fo(g)s Ff(.)141 817 y Fp(It)31 b(can)f(b)s(e)g(sho) m(wn)g(that)h Fo(f)j Fm(\026)25 b Fo(g)34 b Fp(if)c(and)f(only)h(if) 1148 934 y Fj(Z)1199 1140 y Fi(R)1260 1121 y Fe(N)1336 1058 y Fp(\010\()p Fm(j)p Fo(f)10 b Fp(\()p Fo(x)p Fp(\))p Fm(j)p Fp(\))15 b(d)p Fo(x)41 b Fm(\024)1969 934 y Fj(Z)2020 1140 y Fi(R)2081 1121 y Fe(N)2158 1058 y Fp(\010\()p Fm(j)p Fo(g)s Fp(\()p Fo(x)p Fp(\))p Fm(j)p Fp(\))15 b(d)p Fo(x)0 1308 y Fp(for)34 b(all)f(con)m(v)m(ex)j(functions)d(\010)f (:)g([0)p Fo(;)15 b Fp(+)p Fm(1)p Fp(\))33 b Fm(!)f Fp([0)p Fo(;)15 b Fp(+)p Fm(1)p Fp(\))35 b(with)e(\010\(0\))g(=)f(0,)k(see)f ([1].)53 b(In)34 b(particular,)g(if)f Fo(f)41 b Fm(\026)32 b Fo(g)0 1421 y Fp(and)e Fo(g)f Fm(2)c Fo(L)397 1388 y Fk(1)436 1421 y Fp(\()p Fl(R)549 1388 y Fn(N)617 1421 y Fp(\))20 b Fm(\\)g Fo(L)815 1388 y Fg(1)890 1421 y Fp(\()p Fl(R)1003 1388 y Fn(N)1071 1421 y Fp(\),)31 b(then)f Fm(k)p Fo(f)10 b Fm(k)1514 1435 y Fn(L)1562 1416 y Fe(p)1627 1421 y Fm(\024)25 b(k)p Fo(g)s Fm(k)1859 1435 y Fn(L)1907 1416 y Fe(p)1980 1421 y Fp(for)30 b(an)m(y)g Fo(p)25 b Fm(\025)g Fp(1.)141 1534 y(The)h(uniqueness)e(pro)s(of)h(in)g (Section)h(5)h(will)d(b)s(e)h(based)h(on)g(t)m(w)m(o)i(prop)s(erties)d (of)h(the)h(domination)d(relation)0 1647 y(whic)m(h)33 b(w)m(e)h(no)m(w)g(describ)s(e.)50 b(These)34 b(results)f(are)h(rather) g(standard,)g(and)g(the)g(pro)s(ofs)f(will)e(b)s(e)j(outlined)e(for)0 1759 y(completeness)e(only)-8 b(.)0 1972 y Fl(Prop)s(osition)36 b(4.2)46 b Ff(L)-5 b(et)33 b Fo(f)5 b(;)15 b(g)29 b Fp(:)c Fl(R)1191 1939 y Fn(N)1284 1972 y Fm(!)g Fp([0)p Fo(;)15 b Fp(+)p Fm(1)p Fp(\))34 b Ff(b)-5 b(e)32 b(c)-5 b(ontinuous)34 b(and)g(inte)-5 b(gr)g(able)33 b(functions)g(satisfying:)93 2108 y(a\))g Fo(f)i Fm(\026)25 b Fo(g)s Ff(;)93 2245 y(b\))32 b Fo(g)d Fp(=)c Fo(g)418 2212 y Fk(#)482 2245 y Ff(;)93 2382 y(c\))204 2308 y Fj(R)247 2413 y Fi(R)308 2395 y Fe(N)385 2382 y Fo(f)10 b Fp(\()p Fo(x)p Fp(\))15 b(d)p Fo(x)25 b Fp(=)801 2308 y Fj(R)844 2413 y Fi(R)905 2395 y Fe(N)982 2382 y Fo(g)s Fp(\()p Fo(x)p Fp(\))15 b(d)p Fo(x)p Ff(;)93 2518 y(d\))209 2445 y Fj(R)252 2550 y Fi(R)313 2531 y Fe(N)390 2518 y Fm(j)p Fo(x)p Fm(j)492 2485 y Fn(N)560 2518 y Fo(f)10 b Fp(\()p Fo(x)p Fp(\))15 b(d)p Fo(x)24 b Fp(=)975 2445 y Fj(R)1018 2550 y Fi(R)1079 2531 y Fe(N)1156 2518 y Fm(j)p Fo(x)p Fm(j)1258 2485 y Fn(N)1326 2518 y Fo(g)s Fp(\()p Fo(x)p Fp(\))15 b(d)p Fo(x)26 b(<)f Fm(1)p Ff(.)0 2655 y(Then)33 b Fo(f)i Fp(=)24 b Fo(g)s Ff(.)0 2867 y Fl(Remark)34 b(4.3)46 b Ff(As)37 b(is)g(cle)-5 b(ar)37 b(fr)-5 b(om)38 b(the)f(pr)-5 b(o)g(of,)40 b(the)d(same)h(r)-5 b(esult)37 b(holds)i(if)d Fm(j)p Fo(x)p Fm(j)2753 2834 y Fn(N)2858 2867 y Ff(is)g(r)-5 b(eplac)g(e)g(d)40 b(by)c Fo(')p Fp(\()p Fm(j)p Fo(x)p Fm(j)p Fp(\))j Ff(in)0 2980 y(assumption)31 b(d\),)g(wher)-5 b(e)30 b Fo(')g Ff(is)g(any)g(c)-5 b(ontinuous,)31 b(p)-5 b(ositive,)31 b(and)f(strictly)h(incr)-5 b(e)g(asing)30 b(function)g(on)g Fp([0)p Fo(;)15 b Fp(+)p Fm(1)p Fp(\))p Ff(.)0 3193 y Fl(Pro)s(of:)36 b Fp(W)-8 b(e)31 b(\014rst)f(observ)m(e)h (that)1102 3292 y Fj(Z)1153 3498 y Fi(R)1214 3479 y Fe(N)1290 3416 y Fm(j)p Fo(x)p Fm(j)1392 3378 y Fn(N)1460 3416 y Fo(f)1515 3378 y Fk(#)1577 3416 y Fp(\()p Fo(x)p Fp(\))15 b(d)p Fo(x)41 b Fm(\024)1969 3292 y Fj(Z)2020 3498 y Fi(R)2081 3479 y Fe(N)2158 3416 y Fm(j)p Fo(x)p Fm(j)2260 3378 y Fn(N)2327 3416 y Fo(f)10 b Fp(\()p Fo(x)p Fp(\))15 b(d)p Fo(x)30 b(;)916 b Fp(\(4.2\))0 3677 y(and)42 b(that)i(equalit)m (y)e(holds)f(in)h(\(4.2\))j(if)c(and)i(only)e(if)h Fo(f)56 b Fp(=)45 b Fo(f)2220 3644 y Fk(#)2282 3677 y Fp(.)78 b(Indeed,)46 b(this)41 b(is)h(ob)m(vious)h(if)e Fo(f)52 b Fp(is)42 b(the)0 3790 y(c)m(haracteristic)30 b(function)e(of)h(a)h(b) s(ounded)d(op)s(en)i(set)h Fo(A)25 b Fm(\032)g Fl(R)2087 3757 y Fn(N)2155 3790 y Fp(,)k(b)s(ecause)h(then)f Fo(f)2806 3757 y Fk(#)2893 3790 y Fp(=)c Fl(1)3041 3804 y Fn(B)3094 3815 y Fe(R)3178 3790 y Fp(where)k Fo(c)3479 3804 y Fn(N)3547 3790 y Fo(R)3617 3757 y Fn(N)3709 3790 y Fp(=)0 3903 y(meas\()p Fo(A)p Fp(\).)42 b(The)30 b(general)g(case)i(follo)m(ws)d (using)g(the)i(\\la)m(y)m(er)g(cak)m(e)h(represen)m(tation")f([16)q(]) 771 4151 y Fo(f)10 b Fp(\()p Fo(x)p Fp(\))40 b(=)1099 4028 y Fj(Z)1190 4054 y Fg(1)1150 4234 y Fk(0)1280 4151 y Fl(1)1332 4170 y Fg(f)p Fn(f)7 b(>t)p Fg(g)1529 4151 y Fp(\()p Fo(x)p Fp(\))15 b(d)p Fo(t)30 b(;)106 b(f)1966 4114 y Fk(#)2029 4151 y Fp(\()p Fo(x)p Fp(\))41 b(=)2303 4028 y Fj(Z)2394 4054 y Fg(1)2353 4234 y Fk(0)2484 4151 y Fl(1)2536 4107 y Fk(#)2536 4184 y Fg(f)p Fn(f)7 b(>t)p Fg(g)2732 4151 y Fp(\()p Fo(x)p Fp(\))15 b(d)p Fo(t)31 b(;)0 4397 y Fp(together)h(with)d(F)-8 b(ubini's)28 b(theorem.)141 4509 y(No)m(w,)d(let)d Fo(h)j Fp(=)g Fo(g)709 4476 y Fg(\003)752 4509 y Fm(\000)s Fo(f)881 4476 y Fg(\003)920 4509 y Fp(,)f(where)d Fo(f)1278 4476 y Fg(\003)1317 4509 y Fo(;)15 b(g)1403 4476 y Fg(\003)1465 4509 y Fp(are)23 b(the)f(nonincreasing)e(rearrangemen)m(ts)i(of)g Fo(f)5 b(;)15 b(g)s Fp(.)38 b(F)-8 b(or)23 b(all)e Fo(R)26 b(>)f Fp(0,)0 4622 y(w)m(e)31 b(ha)m(v)m(e)297 4753 y Fj(Z)347 4959 y Fn(B)400 4970 y Fe(R)470 4877 y Fo(f)525 4839 y Fk(#)587 4877 y Fp(\()p Fo(x)p Fp(\))15 b(d)p Fo(x)41 b Fp(=)979 4753 y Fj(Z)1070 4779 y Fn(c)1101 4790 y Fe(N)1158 4779 y Fn(R)1211 4756 y Fe(N)1030 4959 y Fk(0)1289 4877 y Fo(f)1344 4839 y Fg(\003)1383 4877 y Fp(\()p Fo(s)p Fp(\))15 b(d)p Fo(s)29 b(;)1766 4753 y Fj(Z)1816 4959 y Fn(B)1869 4970 y Fe(R)1939 4877 y Fm(j)p Fo(x)p Fm(j)2041 4839 y Fn(N)2109 4877 y Fo(f)2164 4839 y Fk(#)2226 4877 y Fp(\()p Fo(x)p Fp(\))15 b(d)p Fo(x)41 b Fp(=)2658 4815 y(1)p 2628 4856 107 4 v 2628 4939 a Fo(c)2667 4953 y Fn(N)2760 4753 y Fj(Z)2850 4779 y Fn(c)2881 4790 y Fe(N)2939 4779 y Fn(R)2992 4756 y Fe(N)2810 4959 y Fk(0)3069 4877 y Fo(sf)3167 4839 y Fg(\003)3206 4877 y Fp(\()p Fo(s)p Fp(\))15 b(d)p Fo(s)29 b(:)0 5138 y Fp(Using)h(the)g(\014rst)g(equalit) m(y)-8 b(,)30 b(w)m(e)h(can)g(rewrite)e(assumptions)g(a\))i(and)f(c\))h (as)g(follo)m(ws:)91 5275 y(a'\))227 5202 y Fj(R)288 5228 y Fn(r)270 5307 y Fk(0)341 5275 y Fo(h)p Fp(\()p Fo(s)p Fp(\))15 b(d)p Fo(s)25 b Fm(\025)g Fp(0)31 b(for)f(all)f Fo(r)f(>)d Fp(0,)91 5411 y(c'\))222 5338 y Fj(R)283 5364 y Fg(1)265 5443 y Fk(0)373 5411 y Fo(h)p Fp(\()p Fo(s)p Fp(\))15 b(d)p Fo(s)25 b Fp(=)g(0.)0 5548 y(In)30 b(view)f(of)i (\(4.2\))h(and)e(the)g(second)h(equalit)m(y)-8 b(,)30 b(assumptions)f(b\))h(and)g(d\))g(also)g(imply)1867 5800 y(6)p eop %%Page: 7 7 7 6 bop 91 91 a Fp(d'\))232 18 y Fj(R)293 44 y Fg(1)275 123 y Fk(0)383 91 y Fo(sh)p Fp(\()p Fo(s)p Fp(\))15 b(d)p Fo(s)25 b Fm(\025)g Fp(0,)31 b(with)e(equalit)m(y)h(if)f(and)h(only)f (if)h Fo(f)k Fp(=)25 b Fo(f)2248 58 y Fk(#)2310 91 y Fp(.)141 254 y(Let)31 b Fm(H)q Fp(\()p Fo(r)s Fp(\))25 b(=)618 181 y Fj(R)678 207 y Fn(r)660 286 y Fk(0)731 254 y Fo(h)p Fp(\()p Fo(s)p Fp(\))15 b(d)p Fo(s)26 b Fp(=)f Fm(\000)1213 181 y Fj(R)1273 207 y Fg(1)1256 286 y Fn(r)1363 254 y Fo(h)p Fp(\()p Fo(s)p Fp(\))15 b(d)p Fo(s)25 b Fm(\025)h Fp(0.)41 b(Clearly)-8 b(,)30 b Fo(r)s Fm(H)q Fp(\()p Fo(r)s Fp(\))24 b Fm(\024)2561 181 y Fj(R)2621 207 y Fg(1)2603 286 y Fn(r)2711 254 y Fo(s)p Fm(j)p Fo(h)p Fp(\()p Fo(s)p Fp(\))p Fm(j)15 b Fp(d)p Fo(s)26 b Fm(!)f Fp(0)31 b(as)f Fo(r)e Fm(!)e Fp(+)p Fm(1)p Fp(,)0 367 y(hence)426 378 y Fj(Z)517 404 y Fg(1)476 584 y Fk(0)606 501 y Fo(sh)p Fp(\()p Fo(s)p Fp(\))15 b(d)p Fo(s)20 b Fp(+)1034 378 y Fj(Z)1125 404 y Fg(1)1085 584 y Fk(0)1215 501 y Fm(H)q Fp(\()p Fo(s)p Fp(\))15 b(d)p Fo(s)40 b Fp(=)1666 378 y Fj(Z)1757 404 y Fg(1)1716 584 y Fk(0)1831 501 y Fp(\()p Fo(sh)p Fp(\()p Fo(s)p Fp(\))21 b(+)f Fm(H)q Fp(\()p Fo(s)p Fp(\)\))15 b(d)p Fo(s)40 b Fp(=)g Fo(r)s Fm(H)q Fp(\()p Fo(r)s Fp(\))2908 397 y Fj(\014)2908 451 y(\014)2908 506 y(\014)2938 423 y Fn(r)r Fk(=)p Fg(1)2938 565 y Fn(r)r Fk(=0)3142 501 y Fp(=)g(0)31 b Fo(:)0 725 y Fp(By)44 b(a'\))i(and)d(d'\),)48 b(this)43 b(implies)f(that)1405 652 y Fj(R)1466 678 y 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b(conclude)e(that)h Fo(!)s Fp(\()p Fo(x;)15 b(t)p Fp(\))31 b(=)g(\012\()p Fo(x;)15 b(t)p Fp(\))34 b(for)0 1940 y(all)29 b Fo(x)c Fm(2)g Fl(R)367 1907 y Fk(2)407 1940 y Fp(,)31 b(whic)m(h)e(is)g(the)i(desired)e(result.)2180 b Fc(\003)0 2226 y Fq(References)45 2429 y Fp([1])47 b(A.)30 b(Alvino,)f(P)-8 b(.-L.)31 b(Lions,)e(and)g(G.)h(T)-8 b(rom)m(b)s(etti.)30 b(On)f(optimization)g(problems)f(with)h(prescrib)s (ed)e(rear-)187 2542 y(rangemen)m(ts.)k Ff(Nonline)-5 b(ar)34 b(A)n(nal.)f(T.M.A.)c Fl(13)h Fp(\(1989\),)k(185{220.)45 2729 y([2])47 b(A.)40 b(Alvino,)i(P)-8 b(.-L.)41 b(Lions,)h(and)d(G.)i (T)-8 b(rom)m(b)s(etti.)40 b(Comparison)f(results)g(for)h(elliptic)e (and)h(parab)s(olic)187 2842 y(equations)21 b(via)h(Sc)m(h)m(w)m(arz)g (symmetrization.)f Ff(A)n(nn.)j(Inst.)h(H.)f(Poinc)-5 b(ar)n(\023)-44 b(e)25 b(A)n(nal.)g(Non)g(Lin)n(\023)-44 b(eair)-5 b(e)22 b Fl(7)g Fp(\(1990\),)187 2955 y(37{65.)45 3143 y([3])47 b(A.)40 b(Alvino,)i(P)-8 b(.-L.)41 b(Lions,)h(and)d(G.)i (T)-8 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(orticit)m(y)h(equations)f(in)f(dimensions)e(t)m(w)m(o)k(and)f(three.) 187 5511 y Ff(Comm.)d(Partial)h(Di\013er)-5 b(ential)33 b(Equations)e Fl(19)g Fp(\(1994\),)i(827{872.)1867 5800 y(8)p eop %%Page: 9 9 9 8 bop 0 91 a Fp([10])47 b(G.-H.)28 b(Cottet.)h(Equations)e(de)g(Na)m (vier-Stok)m(es)i(dans)d(le)h(plan)f(a)m(v)m(ec)j(tourbillon)24 b(initial)h(mesure.)i Ff(C.)i(R.)187 204 y(A)-5 b(c)g(ad.)33 b(Sci.)g(Paris)g(S)n(\023)-44 b(er.)32 b(I)h(Math.)e Fl(303)g Fp(\(1986\),)i(105{108.)0 392 y([11])47 b(I.)j(Gallagher)h (and)f(Th.)g(Galla)m(y)-8 b(.)51 b(Uniqueness)e(for)h(the)h(t)m(w)m (o-dimensional)f(Na)m(vier-Stok)m(es)i(equa-)187 505 y(tion)44 b(with)f(a)i(measure)f(as)h(initial)d(v)m(orticit)m(y)-8 b(.)46 b(Preprin)m(t,)g(Ecole)f(P)m(olytec)m(hnique,)j(2004.)f(Av)-5 b(ailable)187 618 y(at)31 b Fa(http://www.arXiv.org/mat)o(h.AP)o(/040)o (629)o(7)p Fp(.)0 805 y([12])47 b(Th.)36 b(Galla)m(y)g(and)g(C.)h(E.)f (W)-8 b(a)m(yne.)39 b(Global)d(stabilit)m(y)f(of)h(v)m(ortex)i (solutions)d(of)i(the)g(t)m(w)m(o-dimensional)187 918 y(Na)m(vier-Stok)m(es)52 b(equation.)e Ff(Comm.)i(Math.)f(Phys.)p Fp(,)56 b(to)51 b(app)s(ear.)f(Preprin)m(t)e(v)m(ersion)i(a)m(v)-5 b(ailable)50 b(at)187 1031 y Fa(http://www.arXiv.org/mat)o(h.A)o(P/04)o (0244)o(9)p Fp(.)0 1219 y([13])d(Y.)32 b(Giga,)h(T.)e(Miy)m(ak)-5 b(a)m(w)m(a,)35 b(and)c(H.)h(Osada.)g(Tw)m(o-dimensional)d(Na)m (vier-Stok)m(es)k(\015o)m(w)f(with)f(measures)187 1332 y(as)f(initial)e(v)m(orticit)m(y)-8 b(.)32 b Ff(A)n(r)-5 b(ch.)32 b(R)-5 b(ational)35 b(Me)-5 b(ch.)33 b(A)n(nal.)d Fl(104)h Fp(\(1988\),)i(223{250.)0 1519 y([14])47 b(M.-H.)28 b(Giga)f(and)g(Y.)g(Giga.)g Fb(Nonlinear)f(partial)f(di\013eren)m(tial) h(equations)g({)i(asymptotic)f(b)s(eha)m(viour)e(of)187 1632 y(solutions)k(and)g(self-similar)f(solutions)p Fp(.)h(Bo)s(ok)i (in)e(preparation.)0 1820 y([15])47 b(T.)33 b(Kato.)h(The)e(Na)m (vier-Stok)m(es)i(equation)f(for)g(an)f(incompressible)e(\015uid)h(in)g Fl(R)2981 1787 y Fk(2)3054 1820 y Fp(with)g(a)i(measure)g(as)187 1933 y(the)d(initial)e(v)m(orticit)m(y)-8 b(.)32 b Ff(Di\013er)-5 b(ential)33 b(Inte)-5 b(gr)g(al)34 b(Equations)d Fl(7)f Fp(\(1994\),)j(949{966.)0 2120 y([16])47 b(E.)26 b(Lieb)f(and)h(M.)h (Loss.)f Fb(Analysis.)f Fp(Graduate)h(Studies)f(in)g(Mathematics)i Fl(14)p Fp(.)g(American)f(Mathemat-)187 2233 y(ical)k(So)s(ciet)m(y)-8 b(,)31 b(Pro)m(vidence,)f(RI,)h(1997.)0 2421 y([17])47 b(H.)c(Osada.)h(Di\013usion)d(pro)s(cesses)i(with)f(generators)i(of)g (generalized)f(div)m(ergence)g(form.)g Ff(J.)h(Math.)187 2534 y(Kyoto)34 b(Univ.)29 b Fl(27)i Fp(\(1987\),)i(597{619.)0 2721 y([18])47 b(G.)30 b(T)-8 b(alen)m(ti.)29 b(Elliptic)d(equations)j (and)g(rearrangemen)m(ts.)h Ff(A)n(nn.)h(Scuola)i(Norm.)f(Sup.)g(Pisa)d Fl(3)h Fp(\(1976\),)187 2834 y(697{718.)0 3022 y([19])47 b(M.)29 b(T)-8 b(a)m(ylor.)28 b Fb(P)m(artial)g(di\013eren)m(tial)f (equations)h(I)s(I.)g(Qualitativ)m(e)g(studies)e(of)j(linear)e (equations)p Fp(.)h(Applied)187 3135 y(Mathematical)j(Sciences)f Fl(116)p Fp(,)i(Springer,)c(New-Y)-8 b(ork,)32 b(1996.)1867 5800 y(9)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0410150125337--