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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 23
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 23, Issue 3, June 2016
  4. Symmetry for a general class of overdetermined elliptic problems
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 23, Issue 5, October 2016
Nonlinear Differential Equations and Applications NoDEA : Volume 23, Issue 4, August 2016
Nonlinear Differential Equations and Applications NoDEA : Volume 23, Issue 3, June 2016
Center cyclicity of a family of quartic polynomial differential system
The one dimensional parabolic p(x)-Laplace equation
Large time behavior and Lyapunov functionals for a nonlocal differential equation
Infinitely many solutions for the spinorial Yamabe problem on the round sphere
Stability of ground-states for a system of M coupled semilinear Schrödinger equations
Symmetry for a general class of overdetermined elliptic problems
A note on the derivation of rigid-plastic models
Random extremal solutions of differential inclusions
Approximation of an optimal control problem in coefficient for variational inequality with anisotropic p-Laplacian
Vanishing dielectric constant regime for the Navier Stokes Maxwell equations
Symmetry of solutions to nonlocal nonlinear boundary value problems in radial sets
A class of history-dependent variational-hemivariational inequalities
Layered solutions for a fractional inhomogeneous Allen–Cahn equation
Stepwise synthesis of constrained controls for single input nonlinear systems of special form
Existence and uniqueness of global strong solutions to fully nonlinear second order elliptic systems
Quasilinear parabolic problem with p(x)-laplacian: existence, uniqueness of weak solutions and stabilization
Nonlinear Differential Equations and Applications NoDEA : Volume 23, Issue 2, April 2016
Nonlinear Differential Equations and Applications NoDEA : Volume 23, Issue 1, February 2016
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Symmetry for a general class of overdetermined elliptic problems

Content Provider SpringerLink
Author Brock, F.
Copyright Year 2016
Abstract Let $${\Omega}$$ a bounded domain in $${\mathbb{R} ^N }$$ , and let $${u\in C^1 (\overline{\Omega})}$$ a weak solution of the following overdetermined BVP: $${-\nabla (g(|\nabla u|)|\nabla u|^{-1} \nabla u)=f(|x|,u)}$$ , $${ u > 0 }$$ in $${\Omega }$$ and $${u=0, \ |\nabla u(x)| =\lambda (|x|)}$$ on $${\partial \Omega }$$ , where $${g\in C([0,+\infty )\cap C^1 ((0,+\infty ) ) }$$ with $${g(0)=0}$$ , $${g'(t) > 0}$$ for $${t > 0}$$ , $${f\in C([0,+\infty ) \times [0, +\infty ) )}$$ , f is nonincreasing in $${|x|}$$ , $${\lambda \in C([0, +\infty )) }$$ and $${\lambda }$$ is positive and nondecreasing. We show that $${\Omega }$$ is a ball and u satisfies some “local” kind of symmetry. The proof is based on the method of continuous Steiner symmetrization.
Ending Page 16
Page Count 16
Starting Page 1
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 3
Volume Number 23
Language English
Publisher Springer International Publishing
Publisher Date 2016-06-07
Publisher Place Cham
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Maximum principles Symmetry of the solution Continuous rearrangement Boundary value problems for second-order elliptic equations Overdetermined boundary value problem Analysis Oscillation, zeros of solutions, mean value theorems, etc. One-parameter continuous families of measure-preserving transformations Nonlinear boundary value problems for linear elliptic equations Nonlinear elliptic equations Degenerate elliptic equation
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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