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Unique continuation for a quasilinear elliptic equation in the plane
Dead core Harnack inequality maximum principle nodal domain p-Laplacian p-harmonic quasilinear elliptic equation
2012/6/27
We consider planar solutions to certain quasilinear elliptic equations subject to the Dirichlet boundary conditions. We show that if the boundary data has finite number of relative maxima and minima t...
Unique continuation and approximate controllability for a degenerate parabolic equation
degenerate parabolic equations unique continuation approximate controllability local Carleman estimate
2011/9/13
Abstract: This paper studies unique continuation for weakly degenerate parabolic equations in one space dimension. A new Carleman estimate of local type is obtained to deduce that all solutions that v...
ON THE UNIQUE CONTINUATION PROPERTIES FOR ELLIPTIC OPERATORS WITH SINGULAR POTENTIALS
doubling property unique continuation Lipschitz domain Kato--Fefferman--Phong s potential
2007/12/11
Let $u$ be a solution to a second order elliptic equation with singular potentials belonging to Kato--Fefferman--Phong's class in Lipschitz domains. An elementary proof of the doubling property for $u...
On the Unique Continuation Property for the Higher Order Nonlinear Schrödinger Equation With Constant Coefficients
Higher order nonlinear Schrö dinger equation unique continuation property
2010/2/26
We solve the unique continuation property: If u is a solution of the higher order nonlinear Schrödinger equation with constant coefficients with t1 < t2 which is sufficiently smooth and such that...