Relaxation of singular functionals defined on Sobolev spaces

Hafedh Ben Belgacem

Displaying similar documents to “Relaxation of singular functionals defined on Sobolev spaces”

Higher order variational problems on two-dimensional domains.

Bildhauer, Michael, Fuchs, Martin (2006)

Annales Academiae Scientiarum Fennicae. Mathematica

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On the representation of effective energy densities

Christopher J. Larsen (2000)

ESAIM: Control, Optimisation and Calculus of Variations

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

Michael Bildhauer, Martin Fuchs (2007)

Commentationes Mathematicae Universitatis Carolinae

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We consider local minimizers $u : ℝ^{2} \supset Ω \to ℝ^{N}$ of variational integrals like $\int_{Ω} [(1 + | \partial_{1} {u |}^{2})^{p / 2} + (1 + | \partial_{2} {u |}^{2})^{q / 2}] d x$ or its degenerate variant $\int_{Ω} [| \partial_{1} {u |}^{p} + | \partial_{2} u |^{q}] d x$ with exponents $2 \leq p < q < \infty$ which do not fall completely in the category studied in Bildhauer M., Fuchs M., Calc. Var. (2003), 177–186. We prove interior $C^{1, α}$ - respectively $C^{1}$ -regularity of $u$ under the condition that $q < 2 p$ . For decomposable variational integrals of arbitrary order a similar result is established by the way extending the work Bildhauer M., Fuchs M., Ann. Acad. Sci. Fenn. Math. (2006), 349–362. ...

Regularity of minimizers for nonconvex vectorial integrals with $p - q$ growth via relaxation methods.

Benedetti, Irene, Mascolo, Elvira (2004)

Abstract and Applied Analysis

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A variational approach to the local character of $G$ -closure : the convex case

Jean-François Babadjian, Marco Barchiesi (2009)

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

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Existence of multiple solutions for quasilinear diagonal elliptic systems.

Squassina, Marco (1999)

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

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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.

Displaying similar documents to “Relaxation of singular functionals defined on Sobolev spaces”

Higher order variational problems on two-dimensional domains.

On the representation of effective energy densities

On the regularity of local minimizers of decomposable variational integrals on domains in ℝ 2

Regularity of minimizers for nonconvex vectorial integrals with p - q growth via relaxation methods.

A variational approach to the local character of G -closure : the convex case

Existence of multiple solutions for quasilinear diagonal elliptic systems.

Optimal partial regularity of minimizers of quasiconvex variational integrals

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

Regularity of minimizers for nonconvex vectorial integrals with $p - q$ growth via relaxation methods.

A variational approach to the local character of $G$ -closure : the convex case