03-22 Adimurthi, Maria J. Esteban

An improved Hardy-Sobolev inequality in $W^{1,p}$ and its application to Schrodinger operator. (350K, postscript) Jan 17, 03

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Abstract. In this paper we prove optimal Hardy-like inequalities for the Schrodinger operator in $W^{1,p}$. That is, the functions under consideration do not satisfy any particular boundary condition at the boundary of the considered domain. The case of the whole space is also treated. As it is usual, the optimality is given by logarithmic perturbation of the limit power potential. Moreover, a surface integral term takes care of the absence of boundary conditions or of the unboundedness of the domain. On the other hand, eigenvalue problems of almost optimal operators related to the above inequalities are analyzed in detail.

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