A spectral method for an elliptic equation with a nonlinear Neumann boundary condition

2018 ◽  
Vol 81 (1) ◽  
pp. 313-344 ◽  
Author(s):  
Kendall Atkinson ◽  
David Chien ◽  
Olaf Hansen
Keyword(s):  
Boundary Condition ◽  
Elliptic Equation ◽  
Spectral Method ◽  
Neumann Boundary Condition ◽  
Neumann Boundary

scholarly journals EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A NEUMANN PROBLEM INVOLVING VARIABLE EXPONENT GROWTH CONDITIONS

2008 ◽  
Vol 50 (3) ◽  
pp. 565-574 ◽  
Author(s):  
MARIA-MAGDALENA BOUREANU ◽  
MIHAI MIHĂILESCU
Keyword(s):  
Boundary Condition ◽  
Elliptic Equation ◽  
Neumann Problem ◽  
Neumann Boundary Condition ◽  
Variable Exponent ◽  
Main Tool ◽  
Neumann Boundary ◽  
Growth Conditions ◽  
Linear Elliptic Equation ◽  
Existence And Multiplicity

AbstractIn this paper we study a non-linear elliptic equation involving p(x)-growth conditions and satisfying a Neumann boundary condition on a bounded domain. For that equation we establish the existence of two solutions using as a main tool an abstract linking argument due to Brézis and Nirenberg.

New solutions for critical Neumann problems in ℝ2

2017 ◽  
Vol 8 (1) ◽  
pp. 615-644
Author(s):  
Shengbing Deng ◽  
Monica Musso
Keyword(s):  
Boundary Condition ◽  
Elliptic Equation ◽  
Small Parameter ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Normal Vector ◽  
Bounded Smooth Domain ◽  
Neumann Problems ◽  
Bounded Smooth ◽  
Outer Normal Vector

Abstract We consider the elliptic equation {-\Delta u+u=0} in a bounded, smooth domain Ω in {\mathbb{R}^{2}} subject to the nonlinear Neumann boundary condition {\frac{\partial u}{\partial\nu}=\lambda ue^{u^{2}}} , where ν denotes the outer normal vector of {\partial\Omega} . Here {\lambda>0} is a small parameter. For any λ small we construct positive solutions concentrating, as {\lambda\to 0} , around points of the boundary of Ω.

scholarly journals Boundary unique continuation theorems under zero Neumann boundary conditions

2005 ◽  
Vol 72 (1) ◽  
pp. 67-85 ◽  
Author(s):  
Xiangxing Tao ◽  
Songyan Zhang
Keyword(s):  
Boundary Condition ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Neumann Boundary Condition ◽  
Unique Continuation ◽  
Neumann Boundary ◽  
Lipschitz Domains ◽  
Singular Potentials ◽  
Order Elliptic Equation ◽  
Second Order Elliptic Equation

Let u be a solution to a second order elliptic equation with singular potentials belonging to the Kato-Fefferman-Phong's class in Lipschitz domains. We prove the boundary unique continuation theorems and the doubling properties for u2 near the boundary under the zero Neumann boundary condition.

Sign in / Sign up

Export Citation Format

Share Document