Size estimates for the weighted p-Laplace equation with one measurement
نویسندگان
چکیده
منابع مشابه
ENCLOSURE METHOD FOR THE p-LAPLACE EQUATION
We study the enclosure method for the p-Calderón problem, which is a nonlinear generalization of the inverse conductivity problem due to Calderón that involves the p-Laplace equation. The method allows one to reconstruct the convex hull of an inclusion in the nonlinear model by using exponentially growing solutions introduced by Wolff. We justify this method for the penetrable obstacle case, wh...
متن کاملEXISTENCE OF SOLUTIONS TO A PARABOLIC p(x)-LAPLACE EQUATION WITH CONVECTION TERM VIA L∞ ESTIMATES
This article is devoted to the study of the existence of weak solutions to an initial and boundary value problem for a parabolic p(x)-Laplace equation with convection term. Using the De Giorgi iteration technique, the authors establish the critical a priori L∞-estimates and thus prove the existence of weak solutions.
متن کاملEigenvalues Estimates for the p-Laplace Operator on Manifolds
The Laplace-Beltrami operator on a Riemannian manifold, its spectral theory and the relations between its first eigenvalue and the geometrical data of the manifold, such as curvatures, diameter, injectivity radius, volume, has been extensively studied in the recent mathematical literature. In the last few years, another operator, called p-Laplacian, arising from problems on Non-Newtonian Fluids...
متن کاملBIFURCATION OF POSITIVE SOLUTIONS FOR THE ONE-DIMENSIONAL (p, q)-LAPLACE EQUATION
In this article, we study the bifurcation of positive solutions for the one-dimensional (p, q)-Laplace equation under Dirichlet boundary conditions. We investigate the shape of the bifurcation diagram and prove that there exist five different types of bifurcation diagrams. As a consequence, we prove the existence of multiple positive solutions and show the uniqueness of positive solutions for a...
متن کاملOptimal Size Estimates for the Inverse Conductivity Problem with One Measurement
We prove upper and lower estimates on the measure of an inclusion D in a conductor Ω in terms of one pair of current and potential boundary measurements. The growth rates of such estimates are essentially best possible.
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: Discrete and Continuous Dynamical Systems - Series B
سال: 2021
ISSN: 1531-3492
DOI: 10.3934/dcdsb.2020188