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Quasi-minima

Mariano Giaquinta, Enrico Giusti (1984)

Annales de l'I.H.P. Analyse non linéaire

Smoothness properties of solutions to the nonlinear Stokes problem with nonautonomous potentials

Dominic Breit (2013)

Commentationes Mathematicae Universitatis Carolinae

We discuss regularity results concerning local minimizers u : n Ω n of variational integrals like Ω { F ( · , ε ( w ) ) - f · w } d x defined on energy classes of solenoidal fields. For the potential F we assume a ( p , q ) -elliptic growth condition. In the situation without x -dependence it is known that minimizers are of class C 1 , α on an open subset Ω 0 of Ω with full measure if q < p n + 2 n (for n = 2 we have Ω 0 = Ω ). In this article we extend this to the case of nonautonomous integrands. Of course our result extends to weak solutions of the corresponding nonlinear...

Some results on semilinear systems on the unbounded space R3.

J. M. Mercier (2000)

Revista Matemática Complutense

We study in this paper some systems, using standard tools devoted to the analysis of semilinear elliptic problems on R3. These systems do not admit any non trivial radial solutions in the E1 E2 = + 1 cases. A first type of solution consists in a ground state of R (-1,-1), exhibited by variational arguments, whose structure is a finite energy perturbation of a non trivial constant solution of R (-1,-1). A second type consists in a radial, oscillating, asymptotically null at infinity solution in the...

Symmetry of local minimizers for the three-dimensional Ginzburg–Landau functional

Vincent Millot, Adriano Pisante (2010)

Journal of the European Mathematical Society

We classify nonconstant entire local minimizers of the standard Ginzburg–Landau functional for maps in H loc 1 ( 3 ; 3 ) satisfying a natural energy bound. Up to translations and rotations,such solutions of the Ginzburg–Landau system are given by an explicit solution equivariant under the action of the orthogonal group.

Topological degree, Jacobian determinants and relaxation

Irene Fonseca, Nicola Fusco, Paolo Marcellini (2005)

Bollettino dell'Unione Matematica Italiana

A characterization of the total variation T V u , Ω of the Jacobian determinant det D u is obtained for some classes of functions u : Ω R n outside the traditional regularity space W 1 , n Ω ; R n . In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous away from a given one point singularity x 0 Ω . Relations between T V u , Ω and the distributional determinant Det D u are established, and an integral representation is obtained for the relaxed energy of certain polyconvex functionals at maps u W 1 , p Ω ; R n W 1 , Ω x 0 ; R n .

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