The Lipschitz continuity of solutions to Dirichlet and Neumann problems for nonlinear elliptic equations, including the p-Laplace equation, is established under minimal integrability assumptions on the data and on the curvature of the boundary of the domain. The case of arbitrary bounded convex domains is also included. The results have new consequences even for the Laplacian. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM.

Global Lipschitz regularity for a class of quasilinear elliptic equations / A.Cianchi; V.Maz'ya. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 36:(2011), pp. 100-133.

Global Lipschitz regularity for a class of quasilinear elliptic equations

CIANCHI, ANDREA;
2011

Abstract

The Lipschitz continuity of solutions to Dirichlet and Neumann problems for nonlinear elliptic equations, including the p-Laplace equation, is established under minimal integrability assumptions on the data and on the curvature of the boundary of the domain. The case of arbitrary bounded convex domains is also included. The results have new consequences even for the Laplacian. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM.
2011
36
100
133
A.Cianchi; V.Maz'ya
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/398534
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