Abstract

We prove a regularity result for weak solutions of nonlinear elliptic problems of the type −div(a(x,∇u))=μ,  u∈W01,1(Ω)-\text{div}(a(x,\nabla u)) = \mu,\ \ u \in W^{1,1}_0(\Omega) using an approximation technique. Here μ\mu is a bounded Radon measure and the operator A(u)=−div(a(x,∇u))A(u) = -\text{div}(a(x,\nabla u)) is assumed to be coercive and monotone, acting between W01,p(Ω)W^{1,p}_0(\Omega) and W0−1,p′(Ω)W^{-1,p'}_0(\Omega).

Author information

Contact details are reproduced from the original publication and may be historical.

Lucio Boccardo

Dipartimento di Matematica, Università di Roma I, P.le A. Moro 2, I-00185 Roma, Italia.

Thierry Gallouet

UMR 128, ENS-Lyon, F-69364 Lyon Cedex 7, France.

References

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Suggested citation

L. Boccardo, T. Gallouet. “Summability of the Solutions of Nonlinear Elliptic Equations with Right Hand Side Measures.” Journal of Convex Analysis 3 (1996), No. 2, 361–365. https://doi.org/10.68381/jca03024

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Published by Heldermann Verlag, 1996. Rights now held by Banach Press.