Some Maximum Principles in Semilinear Elliptic Equations
نویسندگان
چکیده
منابع مشابه
Singular Solutions for some Semilinear Elliptic Equations
We are concerned with the behavior of u near x = O. There are two distinct cases: 1) When p >= N / ( N -2) and (N ~ 3) it has been shown by BR~ZIS & V~RON [9] that u must be smooth at 0 (See also BARAS & PIERRE [1] for a different proof). In other words, isolated singularities are removable. 2) When 1-< p < N / ( N 2) there are solutions of (1) with a singularity at x ---0. Moreover all singula...
متن کاملSome Limiting Situations for Semilinear Elliptic Equations
— The objective of this mini-course is to take a look at a standard semilinear partial differential equation −∆u = λf(u) on which we show the use of some basic tools in the study of elliptic equation. We will mention the maximum principle, barrier method, blow-up analysis, regularity and boot-strap argument, stability, localization and quantification of singularities, Pohozaev identities, movin...
متن کاملNew Maximum Principles for Linear Elliptic Equations
We prove extensions of the estimates of Aleksandrov and Bakel′man for linear elliptic operators in Euclidean space R to inhomogeneous terms in L spaces for q < n. Our estimates depend on restrictions on the ellipticity of the operators determined by certain subcones of the positive cone. We also consider some applications to local pointwise and L estimates.
متن کاملMaximum principles for elliptic dynamic equations
We consider second order partial dynamic operators of the elliptic type on time scales. We establish basic maximum principles and apply them to obtain the uniqueness of Dirichlet boundary value problems for dynamic elliptic equations, eg Poisson equation. Our special cases include the situation in which several variables are continuous and the other discrete. We conclude with open problems, we ...
متن کاملStrong Maximum Principles for Anisotropic Elliptic and Parabolic Equations
We investigate vanishing properties of nonnegative solutions of anisotropic elliptic and parabolic equations. We describe the optimal vanishing sets, and we establish strong maximum principles.
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: Proceedings of the American Mathematical Society
سال: 1986
ISSN: 0002-9939
DOI: 10.2307/2045776