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# Dynamics of Partial Differential Equations

## Volume 12 (2015)

### Number 1

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

Pages: 1 – 12

DOI: https://dx.doi.org/10.4310/DPDE.2015.v12.n1.a1

#### Author

#### Abstract

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

Published 19 March 2015