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Regularity of renormalized solutions to nonlinear elliptic equations away from the support of measure data

Andrea Dall'Aglio, Sergio Segura de León (2019)

Czechoslovak Mathematical Journal

We prove boundedness and continuity for solutions to the Dirichlet problem for the equation - div ( a ( x , u ) ) = h ( x , u ) + μ , in Ω N , where the left-hand side is a Leray-Lions operator from W 0 1 , p ( Ω ) into W - 1 , p ' ( Ω ) with 1 < p < N , h ( x , s ) is a Carathéodory function which grows like | s | p - 1 and μ is a finite Radon measure. We prove that renormalized solutions, though not globally bounded, are Hölder-continuous far from the support of μ .

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