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weak lower semicontinuity (44) 44
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SIAM Review, ISSN 0036-1445, 2017, Volume 59, Issue 4, pp. 703 - 766
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2018, Volume 50, Issue 1, pp. 779 - 809
We study nonlocal variational problems in L-p, like those that appear in peridynamics. The functional object of our study is given by a double integral. We... 
Relaxation | Lower semicontinuity | Peridynamics | Nonlocal variational problems | Young measures | EXISTENCE | MATHEMATICS, APPLIED | VECTOR CALCULUS | lower semicontinuity | relaxation | nonlocal variational problems | BOUNDARY-VALUE-PROBLEMS | PRINCIPLE | MODEL | MINIMIZERS | LAPLACIAN | WEAK LOWER SEMICONTINUITY | FUNCTIONALS | peridynamics
Journal Article
Bulletin des sciences mathématiques, ISSN 0007-4497, 07/2013, Volume 137, Issue 5, pp. 602 - 616
We isolate a general condition, that we call “localization principle”, on the integrand , assumed to be continuous, under which -quasiconvexity with is a... 
[formula omitted]-quasiconvexity | Localization principle | Young measures | Equi-integrability | Weak lower semicontinuity | quasiconvexity
Journal Article
BULLETIN DES SCIENCES MATHEMATIQUES, ISSN 0007-4497, 07/2013, Volume 137, Issue 5, pp. 602 - 616
We isolate a general condition, that we call "localization principle", on the integrand L:M -> [0, infinity], assumed to be continuous, under which... 
MATHEMATICS, APPLIED | SOBOLEV SPACES | Weak lower semicontinuity | CONVERGENCE | Localization principle | MULTIPLE INTEGRALS | Young measures | Equi-integrability | W-1,W-q-quasiconvexity
Journal Article
Evolution Equations and Control Theory, ISSN 2163-2472, 2014, Volume 3, Issue 3, pp. 363 - 372
We prove a lower semicontinuity theorem for a polyconvex functional of integral form, related to maps u : Omega subset of R-n --> R-m in W-1,W-n(Omega;R-m)... 
Jacobian determinants | Lower semicontinuity | Polyconvex integrals | Vector-valued maps | MATHEMATICS | MATHEMATICS, APPLIED | polyconvex integrals | lower semicontinuity | RELAXATION | WEAK LOWER SEMICONTINUITY | ENERGIES | FUNCTIONALS
Journal Article
Journal of Convex Analysis, ISSN 0944-6532, 2010, Volume 17, Issue 1, pp. 183 - 202
Journal Article
Studia Mathematica, ISSN 0039-3223, 2011, Volume 204, Issue 3, pp. 283 - 294
We prove a lower semicontinuity result for variational integrals associated with a given first order elliptic complex, extending, in this general setting, a... 
Polyconvex integrals | Elliptic complexes | Lower semicontinuity | MATHEMATICS | polyconvex integrals | elliptic complexes | lower semicontinuity | WEAK LOWER SEMICONTINUITY | QUASI-CONVEX INTEGRALS | A-QUASICONVEXITY
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 2007, Volume 66, Issue 3, pp. 582 - 590
In this paper, we give a necessary and sufficient condition for a one-dimensional functional to satisfy the so-called (PS)-weak lower semicontinuity property... 
Non-convex variational problem | Young measures | (PS)-weak lower semicontinuity | MATHEMATICS | non-convex variational problem | MATHEMATICS, APPLIED | young measures
Journal Article
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, ISSN 0036-1410, 2018, Volume 50, Issue 1, pp. 1076 - 1119
In this work we completely characterize generalized Young measures generated by sequences of gradients of maps in W-1,W-1(Omega;R-M), where Omega subset of... 
INTEGRAL FUNCTIONALS | MATHEMATICS, APPLIED | free boundary | SEQUENCES | Young measures and their generalizations | lower semicontinuity | quasiconvexity | BOUNDARY | WEAK LOWER SEMICONTINUITY | OSCILLATIONS
Journal Article
Proceedings of the Royal Society of Edinburgh, Section: A Mathematics, ISSN 0308-2105, 6/2001, Volume 131, Issue 3, pp. 519 - 565
Lower semicontinuity and relaxation results in BV are obtained for multiple integrals F(u,) := f(x, u(x), u(x)) dx, u W1,1 (;Rd), where the energy density f... 
MATHEMATICS | MATHEMATICS, APPLIED | WEAK LOWER SEMICONTINUITY | MULTIPLE INTEGRALS | POLYCONVEX INTEGRALS | FUNCTIONALS
Journal Article
Advances in Calculus of Variations, ISSN 1864-8258, 10/2010, Volume 3, Issue 4, pp. 387 - 408
We study weak lower semicontinuity of integral functionals in W-1,W-p under standard p-growth conditions, with integrands whose negative part may have p-growth... 
Quasiconvexity at the boundary | Lower bound | Multiple integrals | Weak lower semicontinuity | MATHEMATICS | MATHEMATICS, APPLIED | QUASICONVEXITY | quasiconvexity at the boundary | lower bound | multiple integrals | GRADIENTS | Integrals | Analysis | Convex domains
Journal Article
ESAIM: Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 4/2010, Volume 16, Issue 2, pp. 457 - 471
We derive sharp necessary conditions for weak sequential lower semicontinuity of integral functionals on Sobolev spaces, with an integrand which only depends... 
Weak lower semicontinuity | Necessary conditions | Scalar integral functionals | MATHEMATICS, APPLIED | necessary conditions | AUTOMATION & CONTROL SYSTEMS | weak lower semicontinuity
Journal Article
Bulletin of the Iranian Mathematical Society, ISSN 1018-6301, 10/2018, Volume 44, Issue 5, pp. 1283 - 1294
This work introduces a remarkable property of enlargements of maximal monotone operators. The basic tool in our analysis is a family of enlargements,... 
Weak | Subdifferential | ε-Subdifferential | lower semicontinuity | Enlargement | MATHEMATICS | epsilon-Subdifferential | MAXIMAL MONOTONE-OPERATORS | Weak-lower semicontinuity | CALCULUS | CONVEX-FUNCTIONS | FAMILY
Journal Article
Indiana University Mathematics Journal, ISSN 0022-2518, 7/2000, Volume 49, Issue 2, pp. 617 - 635
Journal Article
Advances in Calculus of Variations, ISSN 1864-8258, 01/2019, Volume 12, Issue 1, pp. 57 - 84
Journal Article
Indiana University Mathematics Journal, ISSN 0022-2518, 2006, Volume 55, Issue 2, pp. 869 - 894
Journal Article
Indiana University Mathematics Journal, ISSN 0022-2518, 1/2006, Volume 55, Issue 2, pp. 869 - 894
This paper is motivated by a problem suggested in Müller [11] that concerns the weak lower semicontinuity of a smooth integral functional I(u) on a Sobolev... 
Sufficient conditions | Mathematical integrals | Coercivity | Scalars | Matrices | Mathematical functions | Convexity | Sobolev spaces | Banach space | Calculus of variations | YOUNG MEASURES | MATHEMATICS | CONVEXITY | Morrey's quasiconvexity | QUASICONVEXITY | (PS)-weak lower semicontinuity | Ekeland variational principle
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 8/2009, Volume 193, Issue 2, pp. 311 - 337
Journal Article
Bulletin of the Iranian Mathematical Society, ISSN 1017-060X, 10/2018, Volume 44, Issue 5, pp. 1283 - 1294
This work introduces a remarkable property of enlargements of maximal monotone operators. The basic tool in our analysis is a family of enlargements,... 
hbox {Weak}^{}$$ Weak ∗ -lower semicontinuity | Primary 47H05 | varepsilon $$ ε -Subdifferential | Subdifferential | Mathematics, general | Mathematics | 47N10 | Secondary 47H04 | 26E25 | Enlargement
Journal Article
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