scholarly journals On a Class of Anisotropic Nonlinear Elliptic Equations with Variable Exponent

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Guoqing Zhang ◽  
Hongtao Zhang
Keyword(s):  
Weak Solution ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Priori Estimates

Based on truncation technique and priori estimates, we prove the existence and uniqueness of weak solution for a class of anisotropic nonlinear elliptic equations with variable exponentp(x)→growth. Furthermore, we also obtain that the weak solution is locally bounded and regular; that is, the weak solution isLloc∞(Ω)andC1,α(Ω).

A uniqueness principle for up ≤ (−Δ)α 2u in the Euclidean space

2016 ◽  
Vol 18 (06) ◽  
pp. 1650019 ◽  
Author(s):  
Y. Wang ◽  
J. Xiao
Keyword(s):  
Weak Solution ◽  
Euclidean Space ◽  
Fractional Order ◽  
Elliptic Equations ◽  
Differential Inequality ◽  
Nonlinear Elliptic Equations ◽  
Local Behavior ◽  
Nonlinear Elliptic ◽  
Global And Local ◽  
Appl Math

This paper establishes such a uniqueness principle that under [Formula: see text] the fractional order differential inequality [Formula: see text] has the property that if [Formula: see text] then a non-negative weak solution to [Formula: see text] is unique, and if [Formula: see text] then the uniqueness of a non-negative weak solution to [Formula: see text] occurs when and only when [Formula: see text], thereby innovatively generalizing Gidas–Spruck’s result for [Formula: see text] in [Formula: see text] discovered in [B. Gidas and J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 34 (1981) 525–598].

Existence results for the Dirichlet problem of some degenerate nonlinear elliptic equations

2014 ◽  
Vol 20 (2) ◽  
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Nonlinear Elliptic

AbstractIn this paper we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated to the degenerate nonlinear elliptic equations

On some nonlinear elliptic equations involving derivatives of the nonlinearity

1985 ◽  
Vol 100 (3-4) ◽  
pp. 281-294 ◽  
Author(s):  
J. Carrillo ◽  
M. Chipot
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Elliptic Boundary ◽  
Nonlinear Elliptic Equations ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Nonlinear Elliptic ◽  
Image Position ◽  
Derivatives Of

SynopsisWe give some results on existence and uniqueness for the solution of elliptic boundary value problems of typewhen the βi are not necessarily smooth.

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