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Definition and existence of renormalized solutions of elliptic equations with general measure data. (English. Abridged French version) Zbl 0887.35057
Summary: We introduce a new definition of solution for the nonlinear monotone elliptic problem \[ -\text{div}(a(x,\nabla u))= \mu\text{ in }\Omega,\;u=0\text{ on }\partial\Omega, \] where \(\mu\) is a Radon measure with bounded variation on \(\Omega\). We prove the existence of such a solution, a stability result, and partial uniqueness results.

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35R05 PDEs with low regular coefficients and/or low regular data
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