A free boundary problem for p-Laplacian in the plane
نویسندگان
چکیده
منابع مشابه
A FREE-BOUNDARY PROBLEM FOR THE EVOLUTION p-LAPLACIAN EQUATION WITH A COMBUSTION BOUNDARY CONDITION
We study the existence, uniqueness and regularity of solutions of the equation ft = ∆pf = div (|Df | p−2 Df) under over-determined boundary conditions f = 0 and |Df | = 1. We show that if the initial data is concave and Lipschitz with a bounded and convex support, then the problem admits a unique solution which exists until it vanishes identically. Furthermore, the free-boundary of the support ...
متن کاملTHE ONE PHASE FREE BOUNDARY PROBLEM FOR THE p-LAPLACIAN WITH NON-CONSTANT BERNOULLI BOUNDARY CONDITION
Our objective, here, is to generalize our earlier results on the existence of classical convex solution to a free boundary problem with a Bernoullitype boundary gradient condition and with the p-Laplacian as the governing operator. The main theorems of this paper assert that the exterior and the interior free boundary problem with a Bernoulli law, i.e. with a prescribed pressure a(x) on the “fr...
متن کاملExistence solutions for new p-Laplacian fractional boundary value problem with impulsive effects
Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dyn...
متن کاملAn Inverse Problem for the p-Laplacian: Boundary Determination
We study an inverse problem for nonlinear elliptic equations modelled after the p-Laplacian. It is proved that the boundary values of a conductivity coefficient are uniquely determined from boundary measurements given by a nonlinear Dirichletto-Neumann map. The result is constructive and local, and gives a method for determining the coefficient at a boundary point from measurements in a small n...
متن کاملON THE REGULARITY OF THE FREE BOUNDARY IN THE p-LAPLACIAN OBSTACLE PROBLEM
We study the regularity of the free boundary in the obstacle for the p-Laplacian, min { −∆pu, u − φ } = 0 in Ω ⊂ R. Here, ∆pu = div ( |∇u|p−2∇u ) , and p ∈ (1, 2) ∪ (2,∞). Near those free boundary points where ∇φ 6= 0, the operator ∆p is uniformly elliptic and smooth, and hence the free boundary is well understood. However, when ∇φ = 0 then ∆p is singular or degenerate, and nothing was known ab...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2011
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2011.03.027