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

Dominic Breit

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 $q = \frac{3 d}{d + 2}$