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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 $u : ℝ^{n} \supset Ω \to ℝ^{n}$ of variational integrals like $\begin{matrix} \int_{Ω} {F (\cdot, ε (w)) - f \cdot w} d x \end{matrix}$ 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 $q < p \frac{n + 2}{n}$ (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...

Solutions to elliptic systems of Hamiltonian type in $ℝ^{N}$ .

Tintarev, K. (1999)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Some properties of exponentially harmonic maps

James Eells, Luc Lemaire (1992)

Banach Center Publications

Some remark on the nonexistence of positive solutions for some $α, P$ -Laplacian systems.

Alimohammady, M., Koozegar, M. (2008)

The Journal of Nonlinear Sciences and its Applications

Some remarks on the boundary regularity for minima of variational problems with obstacles.

Martin Fuchs (1986)

Manuscripta mathematica

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...

Stable defects of minimizers of constrained variational principles

R. Hardt, D. Kinderlehrer, Fang-Hua Lin (1988)

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

Strongly indefinite functionals with perturbed symmetries and multiple solutions of nonsymmetric elliptic systems.

Clapp, Mónica, Ding, Yanheng, Hernández-Linares, Sergio (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Su alcune questioni di Calcolo delle Variazioni: omogeneizzazione in domini perforati con condizioni di Neumann e rilassamento

Giuseppe Cardone (2000)

Bollettino dell'Unione Matematica Italiana

Superlinear equations and a uniform anti-maximum principle for the multi-Laplacian operator.

Massa, Eugenio (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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 $H_{loc}^{1} (ℝ^{3}; ℝ^{3})$ 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.

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