scholarly journals Characterizations of second order Sobolev spaces

2015 ◽  
Vol 121 ◽  
pp. 241-261 ◽  
Author(s):  
Xiaoyue Cui ◽  
Nguyen Lam ◽  
Guozhen Lu
Keyword(s):  
Sobolev Spaces ◽  
Second Order

scholarly journals On Entropy Solutions of Anisotropic Elliptic Equations with Variable Nonlinearity Indices

2017 ◽  
Vol 63 (3) ◽  
pp. 475-493 ◽  
Author(s):  
L M Kozhevnikova
Keyword(s):  
Dirichlet Problem ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Unbounded Domains ◽  
Second Order ◽  
Entropy Solutions ◽  
Anisotropic Sobolev Spaces ◽  
Right Hand ◽  
Anisotropic Elliptic Equations

For a certain class of second-order anisotropic elliptic equations with variable nonlinearity indices and L1 right-hand side we consider the Dirichlet problem in arbitrary unbounded domains. We prove the existence and uniqueness of entropy solutions in anisotropic Sobolev spaces with variable indices.

Littlewood–Paley Characterizations of Second-Order Sobolev Spaces via Averages on Balls

2016 ◽  
Vol 59 (01) ◽  
pp. 104-118 ◽  
Author(s):  
Ziyi He ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Sobolev Spaces ◽  
Second Order ◽  
Area Function ◽  
Lusin Area Function

Abstract In this paper, the authors characterize second-order Sobolev spaces W2,p(ℝn), with p ∊ [2,∞) and n ∊ N or p ∊ (1, 2) and n ∊ {1, 2, 3}, via the Lusin area function and the Littlewood–Paley g*λ -function in terms of ball means.

Higher order Adams’ inequality with the exact growth condition

2018 ◽  
Vol 20 (06) ◽  
pp. 1750072 ◽  
Author(s):  
Nader Masmoudi ◽  
Federica Sani
Keyword(s):  
Growth Condition ◽  
Sobolev Spaces ◽  
Higher Order ◽  
Sharp Inequality ◽  
Second Order ◽  
Original Form ◽  
Order Case ◽  
Whole Space ◽  
Exact Growth Condition

Adams’ inequality is the complete generalization of the Trudinger–Moser inequality to the case of Sobolev spaces involving higher order derivatives. The failure of the original form of the sharp inequality when the problem is considered on the whole space [Formula: see text] served as a motivation to investigate in the direction of a refined sharp inequality, the so-called Adams’ inequality with the exact growth condition. Due to the difficulties arising in the higher order case from the lack of direct symmetrization techniques, this refined result is known to hold on first- and second-order Sobolev spaces only. We extend the validity of Adams’ inequality with the exact growth to higher order Sobolev spaces.

scholarly journals Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Serena Boccia ◽  
Sara Monsurrò ◽  
Maria Transirico
Keyword(s):  
Uniqueness Theorem ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
A Priori ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Regularity Result ◽  
Second Order ◽  
Order Linear ◽  
A Priori Bound

We study in this paper a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of , . We obtain an a priori bound, and a regularity result from which we deduce a uniqueness theorem.

A priori estimates in Sobolev spaces for a class of hyperbolic operators in presence of transition

2019 ◽  
Vol 16 (02) ◽  
pp. 245-270 ◽  
Author(s):  
Annamaria Barbagallo ◽  
Vincenzo Esposito
Keyword(s):  
Sobolev Spaces ◽  
A Priori Estimates ◽  
A Priori ◽  
Second Order ◽  
Hyperbolic Operators ◽  
Priori Estimates ◽  
Euclidian Space ◽  
Global Nature

We establish several a priori estimates of local or global nature in Sobolev spaces with general exponent [Formula: see text] for a class of second-order hyperbolic operators with double characteristics in presence of a transition in a domain of the Euclidian space [Formula: see text].

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