On the role of lower bounds in characterizations of weak lower semicontinuity of multiple integrals
نویسنده
چکیده
We study weak lower semicontinuity of integral functionals in W 1,p under standard p-growth conditions, with integrands whose negative part may have p-growth as well. MSC 2000: 49J45
منابع مشابه
Lower semicontinuity for parametric set-valued vector equilibrium-like problems
A concept of weak $f$-property for a set-valued mapping is introduced, and then under some suitable assumptions, which do not involve any information about the solution set, the lower semicontinuity of the solution mapping to the parametric set-valued vector equilibrium-like problems are derived by using a density result and scalarization method, where the constraint set $K$...
متن کاملApproximation of Quasiconvex Functions, and Lower Semicontinuity of Multiple Integrals
We study semicontinuity of multiple integrals ~ f~,u,Du)dx~ where the vector-valued function u is defined for xE ~C N with values in ~ . The function f(x,s,~) is assumed to be Carath@odory and quasiconvex in Morrey's sense. We give conditions on the growth of f that guarantee the sequential lower semicontinuity of the given integral in the weak topology 1 N of the Sobolev space H 'P(~;~ ). The ...
متن کاملWeak Lower Semicontinuity for Polyconvex Integrals in the Limit Case
We prove a lower semicontinuity result for polyconvex functionals of the Calculus of Variations along sequences of maps u : Ω ⊂ R → R in W , 2 ≤ m ≤ n, bounded in W 1,m−1 and convergent in L under mild technical conditions but without any extra coercivity assumption on the integrand.
متن کاملThe Sugeno fuzzy integral of concave functions
The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membershipvalue of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is presenthas been well established. Most of the integral inequalities studied in the fuzzy integration context normally considerconditions such as monotonicity or comonotonicity....
متن کاملOn the Lower Semicontinuity of Quasiconvex Integrals
In this paper, dedicated to Neil Trudinger in the occasion of his 70 birthday, we propose a relatively elementary proof of the weak lower semicontinuity in W 1,p of a general integral of the Calculus of Variations of the type (1.1) below with a quasiconvex density function satisfying p-growth conditions. Several comments and references on the related literature, and a subsection devoted to some...
متن کامل