Calculus of Variations and Geometric Measure Theory

E. Davoli - I. Fonseca

Relaxation of p-growth integral functionals under space-dependent differential constraints

created by davoli on 03 Feb 2017
modified on 04 Sep 2020


Published Paper

Inserted: 3 feb 2017
Last Updated: 4 sep 2020

Journal: Trends in Applications of Mathematics to Mechanics.
Year: 2018


A representation formula for the relaxation of integral energies $$(u,v)\mapsto\int{\Omega} f(x,u(x),v(x))\,dx,$$ is obtained, where $f$ satisfies $p$-growth assumptions, $1<p<+\infty$, and the fields $v$ are subjected to space-dependent first order linear differential constraints in the framework of $\mathscr{A}$-quasiconvexity with variable coefficients.