Literature on Nonlocal Equations: Difference between revisions
imported>Nestor (Created page with "== 2011 == {{Citation | last1=Barles | first1=Guy | last2=Chasseigne | first2=Emmanuel | last3=Imbert | first3=Cyril | title=Hölder continuity of solutions of second-order non-...") |
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{{Citation | last3=Rosado | first3=Jesus | last2=Laurent | first2=Thomas | last1=Bertozzi | first1=Andrea | title=Lp theory for the multidimensional aggregation equation | doi=10.1002/cpa.20334 | year=2011 | journal=[[Communications on Pure and Applied Mathematics]] | issn=0010-3640 | volume=64 | issue=1 | pages=45–83}} | {{Citation | last3=Rosado | first3=Jesus | last2=Laurent | first2=Thomas | last1=Bertozzi | first1=Andrea | title=Lp theory for the multidimensional aggregation equation | doi=10.1002/cpa.20334 | year=2011 | journal=[[Communications on Pure and Applied Mathematics]] | issn=0010-3640 | volume=64 | issue=1 | pages=45–83}} | ||
{{Citation | last1=Silvestre | first1=Luis | title=On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusion | url=http://dx.doi.org/10.1016/j.aim.2010.09.007 | doi=10.1016/j.aim.2010.09.007 | year=2011 | journal=Advances in Mathematics | issn=0001-8708 | volume=226 | issue=2 | pages=2020–2039}} | |||
== 2010 == | == 2010 == | ||
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{{Citation | last1=Barlow | first1=Martin T. | last2=Bass | first2=Richard F. | last3=Chen | first3=Zhen-Qing | last4=Kassmann | first4=Moritz | title=Non-local Dirichlet forms and symmetric jump processes | url=http://dx.doi.org/10.1090/S0002-9947-08-04544-3 | doi=10.1090/S0002-9947-08-04544-3 | year=2009 | journal=[[Transactions of the American Mathematical Society]] | issn=0002-9947 | volume=361 | issue=4 | pages=1963–1999}} | {{Citation | last1=Barlow | first1=Martin T. | last2=Bass | first2=Richard F. | last3=Chen | first3=Zhen-Qing | last4=Kassmann | first4=Moritz | title=Non-local Dirichlet forms and symmetric jump processes | url=http://dx.doi.org/10.1090/S0002-9947-08-04544-3 | doi=10.1090/S0002-9947-08-04544-3 | year=2009 | journal=[[Transactions of the American Mathematical Society]] | issn=0002-9947 | volume=361 | issue=4 | pages=1963–1999}} | ||
{{Citation | last1=Constantin | first1=Peter | last2=Wu | first2=Jiahong | title=Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations | url=http://dx.doi.org/10.1016/j.anihpc.2007.10.002 | doi=10.1016/j.anihpc.2007.10.002 | year=2009 | journal=Annales de l'Institut Henri Poincaré. Analyse Non Linéaire | issn=0294-1449 | volume=26 | issue=1 | pages=159–180}} | |||
{{Citation | last1=Kassmann | first1=Moritz | title=A priori estimates for integro-differential operators with measurable kernels | url=http://dx.doi.org/10.1007/s00526-008-0173-6 | doi=10.1007/s00526-008-0173-6 | year=2009 | journal=Calculus of Variations and Partial Differential Equations | issn=0944-2669 | volume=34 | issue=1 | pages=1–21}} | |||
{{Citation | last1=Kiselev | first1=A. | last2=Nazarov | first2=F. | title=A variation on a theme of Caffarelli and Vasseur | year=2009 | journal=Rossiĭskaya Akademiya Nauk. Sankt-Peterburgskoe Otdelenie. Matematicheski\u\i Institut im. V. A. Steklova. Zapiski Nauchnykh Seminarov (POMI) | issn=0373-2703 | volume=370 | pages=58–72}} | |||
== 2008 == | == 2008 == | ||
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== 2007 == | == 2007 == | ||
{{Citation | last1=Bogdan | first1=Krzysztof | last2=Jakubowski | first2=Tomasz | title=Estimates of heat kernel of fractional Laplacian perturbed by gradient operators | url=http://dx.doi.org/10.1007/s00220-006-0178-y | doi=10.1007/s00220-006-0178-y | year=2007 | journal=Communications in Mathematical Physics | issn=0010-3616 | volume=271 | issue=1 | pages=179–198}} | |||
{{Citation | last1=Caffarelli | first1=Luis | last2=Silvestre | first2=Luis | title=An extension problem related to the fractional Laplacian | url=http://dx.doi.org.ezproxy.lib.utexas.edu/10.1080/03605300600987306 | doi=10.1080/03605300600987306 | year=2007 | journal=Communications in Partial Differential Equations | issn=0360-5302 | volume=32 | issue=7 | pages=1245–1260}} | {{Citation | last1=Caffarelli | first1=Luis | last2=Silvestre | first2=Luis | title=An extension problem related to the fractional Laplacian | url=http://dx.doi.org.ezproxy.lib.utexas.edu/10.1080/03605300600987306 | doi=10.1080/03605300600987306 | year=2007 | journal=Communications in Partial Differential Equations | issn=0360-5302 | volume=32 | issue=7 | pages=1245–1260}} | ||
{{Citation | last1=Forcadel | first1=N. | last2=Lio | first2=F. | last3=Cardaliaguet | first3=P. | last4=Monneau | first4=Régis | title=Dislocation dynamics: a non-local moving boundary | publisher=[[Springer-Verlag]] | location=Berlin, New York | year=2007 | journal=Free boundary problems | pages=125–135}} | |||
== 2005 == | == 2005 == | ||
Latest revision as of 21:28, 23 January 2012
2011
Barles, Guy; Chasseigne, Emmanuel; Imbert, Cyril (2011), "Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations", Journal of the European Mathematical Society (JEMS) 13 (1): 1–26, doi:10.4171/JEMS/242, ISSN 1435-9855, http://dx.doi.org/10.4171/JEMS/242
Bertozzi, Andrea; Laurent, Thomas; Rosado, Jesus (2011), "Lp theory for the multidimensional aggregation equation", Communications on Pure and Applied Mathematics 64 (1): 45–83, doi:10.1002/cpa.20334, ISSN 0010-3640
Silvestre, Luis (2011), "On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusion", Advances in Mathematics 226 (2): 2020–2039, doi:10.1016/j.aim.2010.09.007, ISSN 0001-8708, http://dx.doi.org/10.1016/j.aim.2010.09.007
2010
Biler, Piotr; Monneau, Régis; Karch, Grzegorz (2009), "Nonlinear Diffusion of Dislocation Density and Self-Similar Solutions", Communications in Mathematical Physics 294 (1): 145–168, doi:10.1007/s00220-009-0855-8, ISSN 0010-3616
2009
Barlow, Martin T.; Bass, Richard F.; Chen, Zhen-Qing; Kassmann, Moritz (2009), "Non-local Dirichlet forms and symmetric jump processes", Transactions of the American Mathematical Society 361 (4): 1963–1999, doi:10.1090/S0002-9947-08-04544-3, ISSN 0002-9947, http://dx.doi.org/10.1090/S0002-9947-08-04544-3
Constantin, Peter; Wu, Jiahong (2009), "Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations", Annales de l'Institut Henri Poincaré. Analyse Non Linéaire 26 (1): 159–180, doi:10.1016/j.anihpc.2007.10.002, ISSN 0294-1449, http://dx.doi.org/10.1016/j.anihpc.2007.10.002
Kassmann, Moritz (2009), "A priori estimates for integro-differential operators with measurable kernels", Calculus of Variations and Partial Differential Equations 34 (1): 1–21, doi:10.1007/s00526-008-0173-6, ISSN 0944-2669, http://dx.doi.org/10.1007/s00526-008-0173-6
Kiselev, A.; Nazarov, F. (2009), "A variation on a theme of Caffarelli and Vasseur", Rossiĭskaya Akademiya Nauk. Sankt-Peterburgskoe Otdelenie. Matematicheski\u\i Institut im. V. A. Steklova. Zapiski Nauchnykh Seminarov (POMI) 370: 58–72, ISSN 0373-2703
2008
Barles, G.; Chasseigne, Emmanuel; Imbert, Cyril (2008), "On the Dirichlet problem for second-order elliptic integro-differential equations", Indiana University Mathematics Journal 57 (1): 213–246, doi:10.1512/iumj.2008.57.3315, ISSN 0022-2518, http://dx.doi.org/10.1512/iumj.2008.57.3315
Barles, Guy; Imbert, Cyril (2008), "Second-order elliptic integro-differential equations: viscosity solutions' theory revisited", Annales de l'Institut Henri Poincaré. Analyse Non Linéaire 25 (3): 567–585, doi:10.1016/j.anihpc.2007.02.007, ISSN 0294-1449, http://dx.doi.org/10.1016/j.anihpc.2007.02.007
Caffarelli, Luis; Salsa, Sandro; Silvestre, Luis (2008), "Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian", Inventiones Mathematicae 171 (2): 425–461, doi:10.1007/s00222-007-0086-6, ISSN 0020-9910, http://dx.doi.org/10.1007/s00222-007-0086-6
2007
Bogdan, Krzysztof; Jakubowski, Tomasz (2007), "Estimates of heat kernel of fractional Laplacian perturbed by gradient operators", Communications in Mathematical Physics 271 (1): 179–198, doi:10.1007/s00220-006-0178-y, ISSN 0010-3616, http://dx.doi.org/10.1007/s00220-006-0178-y
Caffarelli, Luis; Silvestre, Luis (2007), "An extension problem related to the fractional Laplacian", Communications in Partial Differential Equations 32 (7): 1245–1260, doi:10.1080/03605300600987306, ISSN 0360-5302, http://dx.doi.org.ezproxy.lib.utexas.edu/10.1080/03605300600987306
Forcadel, N.; Lio, F.; Cardaliaguet, P.; Monneau, Régis (2007), "Dislocation dynamics: a non-local moving boundary", Free boundary problems (Berlin, New York: Springer-Verlag): 125–135
2005
Bass, Richard F.; Kassmann, Moritz (2005), "Harnack inequalities for non-local operators of variable order", Transactions of the American Mathematical Society 357 (2): 837–850, doi:10.1090/S0002-9947-04-03549-4, ISSN 0002-9947, http://dx.doi.org/10.1090/S0002-9947-04-03549-4
2002
Bass, Richard F.; Levin, David A. (2002), "Harnack inequalities for jump processes", Potential Analysis. An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis 17 (4): 375–388, doi:10.1023/A:1016378210944, ISSN 0926-2601, http://dx.doi.org/10.1023/A:1016378210944