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Higher order finite element approximation of a quasilinear elliptic boundary value problem of a non-monotone type

Liping Liu, Michal Křížek, Pekka Neittaanmäki (1996)

Applications of Mathematics

A nonlinear elliptic partial differential equation with homogeneous Dirichlet boundary conditions is examined. The problem describes for instance a stationary heat conduction in nonlinear inhomogeneous and anisotropic media. For finite elements of degree k 1 we prove the optimal rates of convergence 𝒪 ( h k ) in the H 1 -norm and 𝒪 ( h k + 1 ) in the L 2 -norm provided the true solution is sufficiently smooth. Considerations are restricted to domains with polyhedral boundaries. Numerical integration is not taken into account....

Higher regularity for nonlinear oblique derivative problems in Lipschitz domains

Gary M. Lieberman (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

There is a long history of studying nonlinear boundary value problems for elliptic differential equations in a domain with sufficiently smooth boundary. In this paper, we show that the gradient of the solution of such a problem is continuous when a directional derivative is prescribed on the boundary of a Lipschitz domain for a large class of nonlinear equations under weak conditions on the data of the problem. The class of equations includes linear equations with fairly rough coefficients as well...

Hypersurfaces of constant curvature in hyperbolic space II

Bo Guan, Joel Spruck (2010)

Journal of the European Mathematical Society

This is the second of a series of papers in which we investigate the problem of finding, in hyperbolic space, complete hypersurfaces of constant curvature with a prescribed asymptotic boundary at infinity for a general class of curvature functions. In this paper we focus on graphs over a domain with nonnegative mean curvature.

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