Journal ArticleDOI
Existence of classical solutions to a free boundary problem for the p-Laplace operator: (II) the interior convex case
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In this paper, the existence of convex classical solutions for a Bernoulli-type free boundary problem in the interior of a convex domain is proved, where the governing operator is the p-Laplac operator.Abstract:
In this paper, we prove the existence of convex classical solutions for a Bernoulli-type free boundary problem, in the interior of a convex domain. The governing operator considered is the p-Laplac ...read more
Citations
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Journal ArticleDOI
A minimum problem with free boundary for a degenerate quasilinear operator
TL;DR: In this article, the p-Laplace operator was shown to have near flat points in the free boundary of the p Laplace operator in the Alt-Caffarelli type minimum problem.
Journal ArticleDOI
Wulff shape characterizations in overdetermined anisotropic elliptic problems
Chiara Bianchini,Giulio Ciraolo +1 more
TL;DR: In this article, the authors studied some overdetermined problems for possibly anisotropic degenerate elliptic PDEs, including the well-known Serrin's overdetermined problem, and proved the corresponding Wulff shape charact...
Journal ArticleDOI
A singular perturbation problem for the p-Laplace operator
TL;DR: In this article, a uniform Lipschitz regularity of uniformly bounded solutions for the singular perturbation problem was shown. But the uniform Lipinski regularity was not shown for the stationary case of a combus- tion problem with a nonlinearity of power type.
Journal ArticleDOI
Fast Numerical Methods for Bernoulli Free Boundary Problems
TL;DR: The numerical solution of the free boundary Bernoulli problem is addressed and an iterative method based on a level-set formulation and boundary element method is proposed.
Journal ArticleDOI
The one phase free boundary problem for the p-Laplacian with non-constant Bernoulli boundary condition
TL;DR: In this paper, it was shown that the exterior and interior free boundary problem with a Bernoulli law, with a prescribed pressure a(x) on the free streamline of the flow, has convex solutions provided the initial domains are convex.
References
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Book
Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
Book
Functions of one complex variable
TL;DR: In this article, the authors defined the boundary values of Riemann maps and defined the corresponding boundary values for bounded analytic functions in the Bergman space of the Dirichlet problem.
Journal ArticleDOI
Existence and regularity for a minimum problem with free boundary
Journal ArticleDOI
Convexity properties of solutions to some classical variational problems
Luis A. Caffarelli,Joel Spruck +1 more
TL;DR: In this article, Convexity properties of solutions to some classical variational problems are discussed. But they do not consider the problem of convexity property of partial differential equations.
A Free Boundary Problem for the p-Laplacian: Uniqueness, Convexity, and Successive Approximation of Solutions
Andrew F. Acker,R. Meyer +1 more
TL;DR: In this article, the authors prove convergence of a trial free boundary method to a classical solution of a Bernoulli-type free boundary problem for the p-Laplace equation, 1 < p < ∞.
Related Papers (5)
Existence of classical solutions to a free boundary problem for the p-Laplace operator : (I) the exterior convex case
Bernoulli's free-boundary problem, qualitative theory and numerical approximation.
M. Flucher,Martin Rumpf +1 more