Boundary higher integrability for the gradient of distributional solutions of nonlinear systems

Daniela Giachetti; Rosanna Schianchi

ArticleOriginal scientific text

Title

Boundary higher integrability for the gradient of distributional solutions of nonlinear systems

Authors ¹, ¹

Affiliations

Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Facoltà di Ingegneria, Università di Roma "La Sapienza", Via A. Scarpa 16, 00161 Roma, Italy

Abstract

We consider distributional solutions to the Dirichlet problem for nonlinear elliptic systems of the type

{\div A (x, u, D u) = \div f \in Ω, u - u_{0} \in W^{1, r}_0 (Ω)

with r less than the natural exponent p which appears in the coercivity and growth assumptions for the operator A. We prove that

D u \in W^{1, p} (Ω)

if |r-p| is small enough.

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Title

Boundary higher integrability for the gradient of distributional solutions of nonlinear systems

Affiliations

Abstract

Bibliography