Differential and Integral Equations

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

M. Di Giampaolo and F. Leonetti

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356059715

Mathematical Reviews number (MathSciNet)
MR2174977

Zentralblatt MATH identifier
1212.35179

Subjects
Primary: 35R05: Partial differential equations with discontinuous coefficients or data
Secondary: 35B65: Smoothness and regularity of solutions 35D10 35J15: Second-order elliptic equations

Citation

Di Giampaolo, M.; Leonetti, F. Boundedness of weak solutions to some linear elliptic equations with measure data. Differential Integral Equations 18 (2005), no. 12, 1371--1382. https://projecteuclid.org/euclid.die/1356059715


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