On the regularity of local minimizers of decomposable variational integrals on domains in $\mathbb {R}^2$

Michael Bildhauer; Martin Fuchs

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Higher order variational problems on two-dimensional domains.

Bildhauer, Michael, Fuchs, Martin (2006)

Annales Academiae Scientiarum Fennicae. Mathematica

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

Dominic Breit (2013)

Commentationes Mathematicae Universitatis Carolinae

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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...

On the existence of weak solutions for degenerate systems of variational inequalities with critical growth

Martin Fuchs (1994)

Commentationes Mathematicae Universitatis Carolinae

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We prove the existence of solutions to systems of degenerate variational inequalities.

Optimal partial regularity of minimizers of quasiconvex variational integrals

Christoph Hamburger (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove partial regularity with optimal Hölder exponent of vector-valued minimizers of the quasiconvex variational integral $\int F (x, u, D u) d x$ under polynomial growth. We employ the indirect method of the bilinear form.

Degenerate elliptic equation involving a subcritical Sobolev exponent.

Chabrowski, J. (1996)

Portugaliae Mathematica

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Displaying similar documents to “On the regularity of local minimizers of decomposable variational integrals on domains in ℝ 2 ”

Higher order variational problems on two-dimensional domains.

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

On the existence of weak solutions for degenerate systems of variational inequalities with critical growth

Optimal partial regularity of minimizers of quasiconvex variational integrals

Degenerate elliptic equation involving a subcritical Sobolev exponent.

Displaying similar documents to “On the regularity of local minimizers of decomposable variational integrals on domains in $ℝ^{2}$ ”