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

Dominic Breit

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Displaying similar documents to “Smoothness properties of solutions to the nonlinear Stokes problem with nonautonomous potentials”

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. ...

Higher order variational problems on two-dimensional domains.

Bildhauer, Michael, Fuchs, Martin (2006)

Annales Academiae Scientiarum Fennicae. Mathematica

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Interior regularity of weak solutions to the equations of a stationary motion of a non-Newtonian fluid with shear-dependent viscosity. The case $q = \frac{3 d}{d + 2}$

Jörg Wolf (2007)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we consider weak solutions $𝐮 : Ω \to ℝ^{d}$ to the equations of stationary motion of a fluid with shear dependent viscosity in a bounded domain $Ω \subset ℝ^{d}$ ( $d = 2$ or $d = 3$ ). For the critical case $q = \frac{3 d}{d + 2}$ we prove the higher integrability of $\nabla 𝐮$ which forms the basis for applying the method of differences in order to get fractional differentiability of $\nabla 𝐮$ . From this we show the existence of second order weak derivatives of $u$ .

Displaying similar documents to “Smoothness properties of solutions to the nonlinear Stokes problem with nonautonomous potentials”

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

Higher order variational problems on two-dimensional domains.

Interior regularity of weak solutions to the equations of a stationary motion of a non-Newtonian fluid with shear-dependent viscosity. The case q = 3 d d + 2

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

Interior regularity of weak solutions to the equations of a stationary motion of a non-Newtonian fluid with shear-dependent viscosity. The case $q = \frac{3 d}{d + 2}$