scholarly journals Poincaré inequalities and Neumann problems for the variable exponent setting

2021 ◽  
Vol 4 (5) ◽  
pp. 1-22
Author(s):  
David Cruz-Uribe ◽  
◽  
Michael Penrod ◽  
Scott Rodney ◽  
Keyword(s):  
Variable Exponent ◽  
Growth Conditions ◽  
Linear Elliptic Equation ◽  
Poincaré Inequalities ◽  
Neumann Problems ◽  
Variable Exponent Spaces ◽  
Nonstandard Growth ◽  
Poincare Inequalities ◽  
Nonstandard Growth Conditions ◽  
Weighted Poincaré Inequalities

<abstract><p>In an earlier paper, Cruz-Uribe, Rodney and Rosta proved an equivalence between weighted Poincaré inequalities and the existence of weak solutions to a family of Neumann problems related to a degenerate $ p $-Laplacian. Here we prove a similar equivalence between Poincaré inequalities in variable exponent spaces and solutions to a degenerate $ {p(\cdot)} $-Laplacian, a non-linear elliptic equation with nonstandard growth conditions.</p></abstract>

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.

scholarly journals Multiplicity results for nonlocal elliptic transmission problem with variable exponent

2014 ◽  
Vol 33 (2) ◽  
pp. 187-201
Author(s):  
Abdesslem Ayoujil ◽  
Mimoun Moussaoui
Keyword(s):  
Variational Principle ◽  
Nonlinear Equations ◽  
Weak Solutions ◽  
Variable Exponent ◽  
Mountain Pass Theorem ◽  
Growth Conditions ◽  
Transmission Problem ◽  
Multiplicity Results ◽  
Nonstandard Growth ◽  
Nonstandard Growth Conditions

In this paper, a transmission problem given by a system of two nonlinear equations of p(x)-Kirchho type with nonstandard growth conditions are studied. Using the mountain pass theorem combined with the Ekeland's variational principle, we obtain at least two distinct, non-trivial weak solutions.

scholarly journals A remark on optimal weighted Poincaré inequalities for convex domains

2012 ◽  
Vol 23 (4) ◽  
pp. 467-475 ◽  
Author(s):  
Vincenzo Ferone ◽  
Carlo Nitsch ◽  
Cristina Trombetti
Keyword(s):  
Convex Domains ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Weighted Poincaré Inequalities

Some weighted Poincare inequalities

2009 ◽  
Vol 58 (4) ◽  
pp. 1619-1638 ◽  
Author(s):  
Fausto Ferrari ◽  
Enrico Valdinoci
Keyword(s):  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Weighted Poincaré Inequalities
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