Journal ArticleDOI
Optimal Regularity of Lower-Dimensional Obstacle Problems
Reads0
Chats0
TLDR
In this paper, it was shown that the solution of the bounding box problem has the optimal regularity, C 1, 1/2, in any space dimension, and this bound depends only on the local L 2-norm of the solution.Abstract:
In this paper, we prove that solutions to the “boundary obstacle problem” have the optimal regularity, C1,1/2, in any space dimension. This bound depends only on the local L2-norm of the solution. Main ingredients in the proof are the quasiconvexity of the solution and a monotonicity formula for an appropriate weighted average of the local energy of the normal derivative of the solution. Bibliography: 8 titles.read more
Citations
More filters
Journal ArticleDOI
Regularity of the obstacle problem for a fractional power of the laplace operator
TL;DR: In this article, the authors studied the problem of finding the optimal regularity result for the contact set of a function ϕ and s ∈ (0, 1) when ϕ is C 1,s or smoother, and showed that the solution u is in the space c 1,α for every α < s.
Journal ArticleDOI
Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
TL;DR: In this paper, a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem is presented. But this characterization is restricted to thin obstacle problems.
Journal ArticleDOI
Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian
TL;DR: In this paper, a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem is presented. But this characterization is restricted to thin obstacle problems.
Journal ArticleDOI
Nonlinear Porous Medium Flow with Fractional Potential Pressure
TL;DR: In this paper, the authors studied a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator and proved the existence of weak and bounded solutions that propagate with finite speed.
Book ChapterDOI
Nonlinear Diffusion with Fractional Laplacian Operators
TL;DR: In this article, the authors describe two models of flow in porous media including nonlocal (long-range) diffusion effects, based on Darcy's law and inverse fractional Laplacian operator, and prove existence of solutions that propagate with finite speed.
References
More filters
Journal ArticleDOI
Further regularity for the signorini problem
TL;DR: In this article, the signorini problem has been studied in the context of Partial Differential Equations (PDE), and the authors show that it is possible to solve it with regularity.
Journal ArticleDOI
Regularity of the solution of an evolution problem with inequalities on the boundary
TL;DR: In this paper, the regularity of the solution of an evolution problem with inequalities on the boundary is investigated and shown to be a function of the complexity of the problem and its complexity.
Journal ArticleDOI
Regularity of the solution of the quasi variational inequality for the impulse control problem, II
TL;DR: In this paper, the authors studied the regularity of the solution of the quasi variational inequality for the impulse control problem and showed that it is not a special case of variational inequalities.