Second order differentiability of integral functionals on Sobolev spaces and L2-spaces.

1993 ◽  
Vol 1993 (436) ◽  
pp. 1-18 ◽  
Keyword(s):  
Sobolev Spaces ◽  
Second Order ◽  
Integral Functionals

scholarly journals Second-order subgradients of convex integral functionals

1999 ◽  
Vol 351 (9) ◽  
pp. 3687-3711 ◽  
Author(s):  
Mohammed Moussaoui ◽  
Alberto Seeger
Keyword(s):  
Second Order ◽  
Integral Functionals

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.

scholarly journals Minimization of nonsmooth integral functionals

1992 ◽  
Vol 15 (4) ◽  
pp. 673-679
Author(s):  
Nikolaos S. Papageorgiou ◽  
Apostolos S. Papageorgiou
Keyword(s):  
Sobolev Spaces ◽  
Convex Analysis ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Integral Functionals ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Sufficient Conditions For Optimality ◽  
Necessary And Sufficient

In this paper we examine optimization problems involving multidimensional nonsmooth integral functionals defined on Sobolev spaces. We obtain necessary and sufficient conditions for optimality in convex, finite dimensional problems using techniques from convex analysis and in nonconvex, finite dimensional problems, using the subdifferential of Clarke. We also consider problems with infinite dimensional state space and we finally present two examples.

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.

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