Interior regularity of space derivatives to an evolutionary, symmetric $$\varphi $$φ-Laplacian

@article{Burczak2015InteriorRO,
  title={Interior regularity of space derivatives to an evolutionary, symmetric \$\$\varphi \$\$$\phi$-Laplacian},
  author={Jan Burczak and Petr Kaplick'y},
  journal={Monatshefte f{\"u}r Mathematik},
  year={2015},
  volume={183},
  pages={71-101}
}
We consider the Orlicz-growth generalization to the evolutionary p-Laplacian and to the evolutionary symmetric p-Laplacian. We derive the spatial second-order Caccioppoli-type estimate for a local weak solution to these systems. Our result is new even for the p-case. 
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10 Citations

10 Citations

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Weighted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math>-type regularity estimates for nonlinear parabolic equations with Orlicz growth

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TLDR
The weights obtained in this paper are weighted according to the following criteria: regularity, power, efficiency, and ν.

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References

SHOWING 1-10 OF 38 REFERENCES

Evolutionary, symmetric p-Laplacian. Interior regularity of time derivatives and its consequences

We consider the evolutionary symmetric $p$-Laplacian with safety $1$. By symmetric we mean that the full gradient of $p$-Laplacian is replaced by its symmetric part, which causes breakdown of the…

On the global W2,q regularity for nonlinear N-systems of the p-Laplacian type in n space variables

On Regularity of the Time Derivative for Degenerate Parabolic Systems

We prove regularity estimates for time derivatives of a large class of nonlinear parabolic partial differential systems. This includes the instationary (symmetric) $p$-Laplace system and models for…

Almost everywhere Hölder continuity of gradients to non-diagonal parabolic systems

We present a local almost everywhere C1,α-regularity result for a general class of p-nonlinear non-diagonal parabolic systems. The main part of the considered systems depends on space-time variable,…

On the global regularity for nonlinear systems of the p-Laplacian type

We consider the Dirichlet boundary value problem for nonlinear systems of partial differential equations with p-structure. We choose two representative cases: the "full gradient case", corresponding…

A global nonlinear evolution problem for generalized Newtonian fluids: Local initial regularity of the strong solution

The φ-harmonic approximation and the regularity of φ-harmonic maps

Anisotropic parabolic problems with slowly or rapidly growing terms

We consider an abstract parabolic problem in a framework of maximal monotone graphs, possibly multi-valued with growth conditions formulated with help of an $x-$dependent $N-$function. The main…

Everywhere-regularity for some quasilinear systems with a lack of ellipticity

SummaryIt is shown that the derivatives of the solutions of certain quasilinear degenerate elliptic systems are Hölder-continuous, everywhere, in the interior of the domain. This work generalizes a…

Lq theory for a generalized Stokes System

Regularity properties of solutions to the stationary generalized Stokes system are studied. The extra stress tensor is assumed to have a growth given by some N-function, which includes the situation…