# 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.

## 10 Citations

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

- Mathematics
- 2015

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…

### Obstacle problem for a class of parabolic equations of generalized $p$-Laplacian type

- Mathematics
- 2016

### Higher differentiability for solutions of stationary p‐Stokes systems

- MathematicsMathematische Nachrichten
- 2020

We consider weak solutions (u,π):Ω→Rn×R to stationary p‐Stokes systems of the type −diva(x,Eu)+∇π+[Du]u=f,divu=0in Ω⊂Rn , where the function a(x,ξ) satisfies p‐growth conditions in ξ and depends…

### Existence and smoothness for a class of $n$D models in elasticity theory of small deformations

- Mathematics
- 2016

We consider a model for deformations of a homogeneous isotropic body, whose shear modulus remains constant, but its bulk modulus can be a highly nonlinear function. We show that for a general class…

### Existence and smoothness for a class of d-dimensional models in elasticity theory of small deformations

- Mathematics
- 2018

We consider a model for deformations of a homogeneous isotropic body, whose shear modulus remains constant, but its bulk modulus can be a highly nonlinear function. We show that for a general class…

### Calderón–Zygmund estimates for a class of quasilinear parabolic equations

- MathematicsNonlinear Analysis
- 2018

### Lorentz estimates for a class of nonlinear parabolic systems

- MathematicsJournal of Differential Equations
- 2019

### 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

- Art, ChemistryElectronic Journal of Qualitative Theory of Differential Equations
- 2022

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

### Electronic Journal of Qualitative Theory of Differential Equations

- 2022

## References

SHOWING 1-10 OF 38 REFERENCES

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

- Mathematics
- 2015

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

- Mathematics
- 2012

### On Regularity of the Time Derivative for Degenerate Parabolic Systems

- MathematicsSIAM J. Math. Anal.
- 2015

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

- Mathematics
- 2012

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

- Mathematics
- 2010

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

- MathematicsComput. Math. Appl.
- 2007

### Anisotropic parabolic problems with slowly or rapidly growing terms

- Mathematics
- 2013

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

- Mathematics
- 1983

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

- Mathematics
- 2013

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…