Lower Semicontinuity in SBV for Integrals with Variable Growth
نویسندگان
چکیده
We prove a lower semicontinuity result for free discontinuity energies with a quasiconvex volume term having non standard growth and a surface term.
منابع مشابه
Lower Semicontinuity of Quasi-convex Bulk Energies in SBV and Integral Representation in Dimension Reduction
A result of Larsen concerning the structure of the approximate gradient of certain sequences of functions with Bounded Variation is used to present a short proof of Ambrosio’s lower semicontinuity theorem for quasiconvex bulk energies in SBV . It enables to generalize to the SBV setting the decomposition lemma for scaled gradients in dimension reduction and also to show that, from the point of ...
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 کاملA lower semicontinuity result for polyconvex functionals in SBV
We prove a semicontinuity theorem for an integral functional made up by a polyconvex energy and a surface term. Our result extends to the BV framework a well known result by John Ball.
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 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Math. Analysis
دوره 42 شماره
صفحات -
تاریخ انتشار 2010