Dal Maso, Gianni; Murat, François; Orsina, Luigi; Prignet, Alain Definition and existence of renormalized solutions of elliptic equations with general measure data. (English. Abridged French version) Zbl 0887.35057 C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 5, 481-486 (1997). 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. Cited in 35 Documents 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 PDFBibTeX XMLCite \textit{G. Dal Maso} et al., C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 5, 481--486 (1997; Zbl 0887.35057) Full Text: DOI EuDML