## 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

### Keywords:

Radon measure with bounded variation; stability; uniqueness
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