• Corpus ID: 119641787

# A geometric approach to regularity for nonlinear free boundary problems

@article{Karakhanyan2017AGA,
title={A geometric approach to regularity for nonlinear free boundary problems},
author={Aram L. Karakhanyan},
journal={arXiv: Analysis of PDEs},
year={2017}
}
• A. Karakhanyan
• Published 1 February 2017
• Mathematics
• arXiv: Analysis of PDEs
Let $u$ be a weak solutions of the free boundary problem $\mathcal L u=\lambda_0 \mathcal H^1\lfloor\partial\{u>0\}, u\ge 0$ where $\mathcal L u=\hbox{div}(g(\nabla u)\nabla u)$ and $g(\xi)$ is a given function of $\xi$ satisfying some standard structural conditions. We prove that the free boundary of the weak solutions is continuously differentiable in $\mathbb R^2$. The full regularity of the free boundary is not fully understood even for the $minimizers$ in the simplest case \$g(\xi)=|\xi…

## References

SHOWING 1-10 OF 26 REFERENCES
Full and partial regularity for a class of nonlinear free boundary problems
• A. Karakhanyan
• Mathematics
Annales de l'Institut Henri Poincaré C, Analyse non linéaire
• 2021
Analytical solutions for von Kármán streets of hollow vortices
• Physics
• 2011
New analytical solutions are presented for steadily translating von Karman vortex streets made up of two infinite rows of hollow vortices. First, the solution for a single row of hollow vortices due
Full regularity of the free boundary in a Bernoulli-type problem in two dimensions
• Mathematics
• 2006
In this note we prove that in dimension n = 2 there are no singular points on the free boundary ∂{u > 0}∩Ω in the Bernoulli-type problem governed by the p-Laplace operator
A free boundary problem for quasilinear elliptic equations
• Mathematics
• 1984
L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions
A free boundary problem for quasi-linear elliptic equations
• Mathematics
• 1984
L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions
Classification of the Solutions to an Overdetermined Elliptic Problem in the Plane
We classify the solutions to an overdetermined elliptic problem in the plane in the finite connectivity case. This is achieved by establishing a one-to-one correspondence between the solutions to