A regularity result for a linear elliptic equation with Hardy-type potential

We consider a linear elliptic problem with Dirichlet boundary conditions, with a potential term $b(x)u$ where the potential function $b$ behaves as $\frac{1}{\mathrm{dist}^2 (x, \partial \Omega)}$ close to the boundary. We study the effect of this potential term on the $H^2$ regularity of the solution of the problem. An application to a stationary Fokker-Planck-Smoluchowski equation for FENE models of diluted polymers is given.

Keywords

regularity of partial differential equations, Fokker-Plack-Smoluchowski equations, Hardy-type potential

2010 Mathematics Subject Classification

35H99

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Published 19 March 2015