We discuss various methods of establishing lower semicontinuity of integral functionals. First we show that if original integrand $L$ can be approximated locally uniformly by integrands $L_k$ with $p$ growth such that ($L_k +\Phi)^qc$ converges pointwisely to $(L + \Phi)^qc$ for each $C^{\infty}$regular integrand $\Phi$ with compact support then lower semicontinuity holds in biting sense for the integral functional with the integrand $L$. We isolate condition which is both necessary and sufficient for lower semicontinuity of $p$coercive problems: $p$quasiconvexity and condition (M). Condition (M) means that when approximating linear functions by Sobolev functions the sequence can be replaced (up to subsequence) by functions with the linear boundary data without increase of energy in the limit. It turned out that there is rather simple relaxation theory in the case when condition (M) holds.
You are here
Lower semicontinuity and relaxation for extendedvalued integrands
Research Group:
Mikhail Sychev
Location:
A133
Schedule:
Tuesday, April 24, 2018  16:00
Abstract:
Openings
 Public calls for academic personnel (Permanent positions)
 Professors (Temporary/Researchers/Visiting Professors)
 SISSA Mathematical Fellowships
 Post Doctoral Fellowships
 PhD Scholarships
 Call for Applications (PhD)
 Undergraduate Fellowships
 Postgraduate Fellowships
 Master of Science in Mathematics
 Marie SklodowskaCurie Grants
Upcoming events

Yash Jhaveri
On the (in)stability of the identity map in optimal transportation
Tuesday, April 24, 2018  14:30

Mikhail Sychev
Lower semicontinuity and relaxation for extendedvalued integrands
Tuesday, April 24, 2018  16:00

Christopher J. Larsen
Minimality for limits of unilateral cohesive energy minimizers
Thursday, April 26, 2018  16:00

Riccardo Montalto
Normal form coordinates for the KdV equation near finite gap potentials
Thursday, May 3, 2018  14:30
Today's Lectures

Antonio Lerario
09:00 to 11:00

Luca Heltai
11:00 to 13:00

Gianluigi Rozza
11:00 to 13:00

Fabio Cavalletti
11:00 to 13:00

Ugo Boscain
11:00 to 13:00
Recent publications

G. Dal Maso; C.J. Larsen; R. Toader,Existence for elastodynamic Gr...

F. Cagnetti; G. Dal Maso; L. Scardia; C.I. Zeppieri,Stochastic homogenisation of f...

A. Michelangeli; P.Thanh Nam; A. Olgiati,Ground state energy of mixture...

A. Michelangeli; A. Olgiati,Effective nonlinear spinor dy...