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

Kelbji Sabrina Star
Development of Reduced Order CFD models with ITHACAFV for a nuclear physics application
Wednesday, October 17, 2018  14:00

Giovanni Bellettini
Apparent contours and reconstruction of solid shapes
Thursday, October 18, 2018  16:00

Monica Nonino
Reduced order methods for fluid structure interaction problems and reduction of the Kolmogorov nwidth
Friday, October 19, 2018  14:00

Prof
Andrea Cangiani
Numerical PDEs with general meshes and adaptivity
Wednesday, October 24, 2018  16:00 to 17:00
Today's Lectures

Gianni Dal Maso
09:00 to 11:00

Guido De Philippis
14:00 to 16:00

Alberto Sartori
14:00 to 16:00

Xiao Han
15:30 to 17:30

Enrico Arbarello (Sapienza)
16:00 to 18:30

Luca Heltai  Gianluigi Rozza
16:00 to 18:00
Recent publications

N. Demo; M. Tezzele; G. Rozza,PyDMD: Python Dynamic Mode Dec...

I. Martini; B. Haasdonk; G. Rozza,Certified Reduced Basis Approx...

F. Riva; L. Nardini,Existence and uniqueness of dy...

P. Antonini; S. Azzali; G. Skandalis,{The Baum–Connes conjecture lo...