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Non-homogeneous boundary value conditions for elliptic problems with measure valued right hand side. (Conditions aux limites non homogènes pour des problèmes elliptiques avec second membre mesure.) (French) Zbl 0895.35103

Summary: For \(\Omega\) a smooth open bounded set of \(\mathbb{R}^N\), we study the elliptic problem \(-\text{div} (A(x,u, \nabla u)) =f\) in \({\mathcal D}' (\Omega)\) where \(f\) is a Radon measure, and we show existence of a solution verifying non homogeneous boundary conditions of Neumann, Fourier and Dirichlet.

MSC:

35R05 PDEs with low regular coefficients and/or low regular data
35J60 Nonlinear elliptic equations
35J25 Boundary value problems for second-order elliptic equations
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References:

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