Sobolev spaces with variable exponents on Riemannian manifolds

2013 ◽  
Vol 92 ◽  
pp. 47-59 ◽  
Author(s):  
Michał Gaczkowski ◽  
Przemysław Górka
Keyword(s):  
Sobolev Spaces ◽  
Riemannian Manifolds ◽  
Variable Exponents

scholarly journals Existence and uniqueness of weak solution of p(x)- Laplacian in Sobolev spaces with variable exponents in complete manifolds

Filomat ◽  
2021 ◽  
Vol 35 (5) ◽  
pp. 1453-1463
Author(s):  
Omar Benslimane ◽  
Ahmed Aberqi ◽  
Jaouad Bennouna
Keyword(s):  
Sobolev Spaces ◽  
Riemannian Manifolds ◽  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Polynomial Growth ◽  
Mountain Pass Theorem ◽  
Variable Exponents ◽  
Variable Exponent Sobolev Spaces ◽  
Complete Manifolds ◽  
Laplacian Equations

The paper deals with the existence and uniqueness of a non-trivial solution to non-homogeneous p(x)- Laplacian equations, managed by non polynomial growth operator in the framework of variable exponent Sobolev spaces on Riemannian manifolds. The mountain pass Theorem is used.

scholarly journals The concentration-compactness principles for Ws,p(·,·)(ℝN) and application

2020 ◽  
Vol 10 (1) ◽  
pp. 816-848
Author(s):  
Ky Ho ◽  
Yun-Ho Kim
Keyword(s):  
Sobolev Spaces ◽  
Concentration Compactness ◽  
Variable Exponents ◽  
Fractional Sobolev Spaces ◽  
Nonlocal Problems

Abstract We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems with variable exponents, which is even new for constant exponent case.

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