Gradient boundedness up to the boundary for solutions to Dirichlet and Neumann problems for elliptic systems with Uhlenbeck type structure is established. Nonlinearities of possibly non-polynomial type are allowed, and minimal regularity on the data and on the boundary of the domain is assumed. The case of arbitrary bounded convex domains is also included. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM.
Global Boundedness of the Gradient for a Class of Nonlinear Elliptic Systems / Andrea Cianchi; Vladimir Maz'ya. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 212:(2014), pp. 129-177.
Global Boundedness of the Gradient for a Class of Nonlinear Elliptic Systems
CIANCHI, ANDREA;
2014
Abstract
Gradient boundedness up to the boundary for solutions to Dirichlet and Neumann problems for elliptic systems with Uhlenbeck type structure is established. Nonlinearities of possibly non-polynomial type are allowed, and minimal regularity on the data and on the boundary of the domain is assumed. The case of arbitrary bounded convex domains is also included. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM.
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