Weak Solutions, Elliptic Problems and Sobolev Spaces

2007 ◽  
pp. 125-172
Keyword(s):  
Sobolev Spaces ◽  
Weak Solutions ◽  
Elliptic Problems

scholarly journals Poincaré Inequalities and Neumann Problems for the p-Laplacian

2018 ◽  
Vol 61 (4) ◽  
pp. 738-753 ◽  
Author(s):  
David Cruz-Uribe ◽  
Scott Rodney ◽  
Emily Rosta
Keyword(s):  
Quadratic Form ◽  
Neumann Problem ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Poincaré Inequalities ◽  
Existence Of Weak Solutions ◽  
Neumann Problems ◽  
Poincare Inequalities ◽  
Associated Matrix ◽  
Weighted Poincaré Inequalities

AbstractWe prove an equivalence between weighted Poincaré inequalities and the existence of weak solutions to a Neumann problem related to a degenerate p-Laplacian. The Poincaré inequalities are formulated in the context of degenerate Sobolev spaces defined in terms of a quadratic form, and the associated matrix is the source of the degeneracy in the p-Laplacian.

Existence of two weak solutions for some singular elliptic problems

2015 ◽  
Vol 110 (2) ◽  
pp. 385-393 ◽  
Author(s):  
M. Khodabakhshi ◽  
A. M. Aminpour ◽  
G. A. Afrouzi ◽  
A. Hadjian
Keyword(s):  
Weak Solutions ◽  
Elliptic Problems

Embeddings of weighted Sobolev spaces and degenerate elliptic problems

2017 ◽  
Vol 60 (8) ◽  
pp. 1399-1418 ◽  
Author(s):  
ZongMing Guo ◽  
LinFeng Mei ◽  
FangShu Wan ◽  
XiaoHong Guan
Keyword(s):  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Elliptic Problems ◽  
Degenerate Elliptic

Arbitrarily small weak solutions for a nonlinear eigenvalue problem in Orlicz–Sobolev spaces

2011 ◽  
Vol 165 (3-4) ◽  
pp. 305-318 ◽  
Author(s):  
Gabriele Bonanno ◽  
Giovanni Molica Bisci ◽  
Vicenţiu Rădulescu
Keyword(s):  
Eigenvalue Problem ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Nonlinear Eigenvalue Problem ◽  
Nonlinear Eigenvalue

Two weak solutions for some Kirchhoff-type problem with Neumann boundary condition

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Moloud Makvand Chaharlang ◽  
Abdolrahman Razani
Keyword(s):  
Boundary Condition ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Neumann Boundary Condition ◽  
Mountain Pass Theorem ◽  
Minimum Principle ◽  
Neumann Boundary ◽  
Type Problem ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem

AbstractIn this article we prove the existence of at least two weak solutions for a Kirchhoff-type problem by using the minimum principle, the mountain pass theorem and variational methods in Orlicz–Sobolev spaces.

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