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This manuscript extends the relaxation theory from nonlinear elasticity to electromagnetism and to actions defined on paths of differential forms. The introduction of a gauge allows for a reformulation of the notion of quasiconvexity in Bandyopadhyay et al ...
In this work we give optimal, i.e., necessary and sufficient, conditions for integrals of the calculus of variations to guarantee the existence of solutions-both weak and variational solutions-to the associated L-2-gradient flow. The initial values are mer ...
Let Omega subset of R-n be an open set, A is an element of R-nxn and G : Omega -> R-nxn be given. We look for a solution u : Omega -> R-n of the equation A del u + (del u)(t) A = G We also study the associated Dirichlet problem. (C) 2020 Elsevier Ltd. All ...
In this article we study some necessary and sufficient conditions for the existence of solutions in W-0(1,infinity) (Omega; Lambda(k)) of the differential inclusion d omega is an element of E a.e. in Omega where E subset of Lambda(k+1) is a prescribed set. ...
Let c : A(k-1) -> R+ be convex and Omega subset of R-n be a bounded domain. Let f(0) and f(1) be two closed k-forms on Omega satisfying appropriate boundary conditions. We discuss the minimization of integral(Omega) c (A) dx over a subset of (k - 1)-forms ...
We consider the problem {div u + (a; u) = f in Omega u = u(0) on partial derivative Omega. We show that if curl a (x(0)) not equal for some x(0) epsilon Omega, then the problem is solvable without restriction on f. We also discuss the regularity of the sol ...
Given the contact forms f and g, and the 1-form h, we discuss the existence of a vector field u verifying L-u(f)= d(u (right perpendicular) f)+ u (right perpendicular) df = h. This is closely related to the pullback equation, where we seek for a diffeomorp ...
Walter De Gruyter Gmbh2017
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Let f, g be two closed k-forms over R-n. The pullback equation studies the existence of a diffeomorphism phi : R-n -> R-n such that phi*(g) = f. We prove two types of results. The first one sharpens some of the existing regularity results. The second one d ...
Springer2014
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We study integrals of the form integral(Omega) f (d omega), where 1
European Mathematical Soc2015
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We discuss three types of problems. The first one involves Jacobian equations and the two others involve Hessian equations. We proceed by fixed point, obtaining the results under a smallness assumption. ...
