Differential and Integral Equations

Boundedness of weak solutions to some linear elliptic equations with measure data

Abstract

We prove boundedness of weak solutions $u$ to some linear elliptic equations in divergence form $$-div(a(x)Du(x))=\mu\,.$$ On the right-hand side we have a Radon measure $\mu$ with a suitable decay on balls $0\leq\mu(B(x,\rho))\leq c\rho^{s}.$

Article information

Source
Differential Integral Equations, Volume 18, Number 12 (2005), 1371-1382.

Dates
First available in Project Euclid: 21 December 2012