Titlebook: Calculus of Variations; Filip Rindler Textbook 2018 Springer International Publishing AG, part of Springer Nature 2018 calculus of variati

新鲜

刚开始

Malleable

Obligatory

HAUNT

Quasiconvexitysponding integral functional. Moreover, we proved in Proposition 2.9 that if . or ., then convexity of the integrand is also necessary for weak lower semicontinuity. In the vectorial case (.), however, it turns out that one can find weakly lower semicontinuous integral functionals whose integrands a

死亡率

Polyconvexity Thus, we were led to consider quasiconvex integrands. However, while quasiconvexity is of tremendous importance in the theory of the calculus of variations, our Lower Semicontinuity Theorem . has one major drawback: we needed to require the .-growth bound

侵略

Resistance

Generalized Young Measurester, however, here we proceed in a more abstract way: We first introduce the theory of ., which extends the standard theory of Young measures developed in Chapter .. Besides quantifying oscillations (like classical Young measures), this theory crucially allows one to quantify . as well, thus providi

considerable

xanthelasma

Book 2009ent insight into state-of-the-art developments in this broad and growing ?eld of research. The editors warmly thank all the scientists, who have contributed by their outstanding papers to the quality of this edition. Special thanks go to Jaan Simon for his great help in putting together the manuscri