Abstract We study the regularizing effect of the interaction between the coefficient of the zero order term and the datum in some nonlinear Dirichlet problems. The simplest example is the linear problem View the MathML source Turn MathJax on where Ω is a bounded open set of RN , M is a bounded elliptic matrix and 0≤a(x)∈L1(Ω) . Even if f(x) only belongs to L1(Ω) , the assumption View the MathML source Turn MathJax on implies the existence of a weak solution u belonging to View the MathML source and to L∞(Ω) .
Regularizing effect of the interplay between coefficients in some elliptic equations / David, Arcoya; Boccardo, Lucio. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 268:(2015), pp. 1153-1166. [10.1016/j.jfa.2014.11.011]
Regularizing effect of the interplay between coefficients in some elliptic equations
BOCCARDO, Lucio
2015
Abstract
Abstract We study the regularizing effect of the interaction between the coefficient of the zero order term and the datum in some nonlinear Dirichlet problems. The simplest example is the linear problem View the MathML source Turn MathJax on where Ω is a bounded open set of RN , M is a bounded elliptic matrix and 0≤a(x)∈L1(Ω) . Even if f(x) only belongs to L1(Ω) , the assumption View the MathML source Turn MathJax on implies the existence of a weak solution u belonging to View the MathML source and to L∞(Ω) .File | Dimensione | Formato | |
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Arcoya_Regularizing-effect_2015.pdf
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