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Global Lipschitz Regularity for a Class of Quasilinear Elliptic Equations |
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| Authors: | Andrea Cianchi Vladimir G. Maz'ya |
| Affiliation: | 1. Dipartimento di Matematica U. Dini , Università di Firenze , Firenze, Italy cianchi@unifi.it;3. Department of Mathematical Sciences , University of Liverpool , Liverpool, United Kingdom;4. Department of Mathematics , Link?ping University , Link?ping, Sweden |
| 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. |
| Keywords: | Boundedness of the gradient Convex domains Dirichlet problems Isoperimetric inequalities Lipschitz continuity of solutions Lorentz spaces Neumann problems Nonlinear elliptic equations |