On the computation of crystalline microstructure

M Luskin - Acta numerica, 1996 - cambridge.org
Microstructure is a feature of crystals with multiple symmetry-related energy-minimizing
states. Continuum models have been developed explaining microstructure as the mixture of …

Ss antman je marsden l. sirovich

JKHPHJ Keener, JKBJMA Mielke, CSPKR Sreenivasan - 2005 - Springer
The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

[图书][B] Parametrized measures and variational principles

P Pedregal - 1997 - books.google.com
Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same
compactness properties that finite dimensional spaces do: basically, bounded sequences …

[图书][B] Relaxation in optimization theory and variational calculus

T Roubíček - 2020 - books.google.com
The relaxation method has enjoyed an intensive development during many decades and
this new edition of this comprehensive text reflects in particular the main achievements in the …

Gradient Young measures generated by sequences in Sobolev spaces

D Kinderlehrer, P Pedregal - The Journal of Geometric Analysis, 1994 - Springer
Oscillatory properties of a weak convergent sequence of functions bounded in L p, 1≤
p≤∞, may be summarized by the parametrized measure it generates. When such a …

[图书][B] Implicit partial differential equations

B Dacorogna, P Marcellini - 2012 - books.google.com
Nonlinear partial differential equations has become one of the main tools of mod ern
mathematical analysis; in spite of seemingly contradictory terminology, the subject of …

[图书][B] Variational methods in nonlinear elasticity

P Pedregal - 2000 - SIAM
The underlying mathematical problems in nonlinear elasticity are fascinating. The variational
methods developed to tackle them are even more so. The graduate student and the …

Regularity of quasiconvex envelopes

JM Ball, B Kirchheim, J Kristensen - Calculus of Variations and Partial …, 2000 - Springer
We prove that the quasiconvex envelope of a differentiable function which satisfies natural
growth conditions at infinity is a C^1 function. Without the growth conditions the result fails in …

Functional analysis and applied optimization in Banach spaces

F Botelho - Cham, Switzerland: Springer, 2014 - Springer
The first objective of this work is to present, to some extent, a deep introduction to the basic
concepts on real and functional analysis. In principle, the text is written for applied …

Restrictions on microstructure

K Bhattacharya, NB Firoozye, RD James… - Proceedings of the …, 1994 - cambridge.org
We consider the following question: given a set of matrices with no rank-one connections,
does it support a nontrivial Young measure limit of gradients? Our main results are these:(a) …