Lower semicontinuity of a class of multiple integrals below the growth exponent
نویسندگان
چکیده
منابع مشابه
Approximation 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 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 کاملLower Semicontinuity in SBV for Integrals with Variable Growth
We prove a lower semicontinuity result for free discontinuity energies with a quasiconvex volume term having non standard growth and a surface term.
متن کاملOn the role of lower bounds in characterizations of weak lower semicontinuity of multiple integrals
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
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de la faculté des sciences de Toulouse Mathématiques
سال: 2001
ISSN: 0240-2963
DOI: 10.5802/afst.993