# Harnack inequality and continuity of solutions to quasi-linear degenerate parabolic equations with coefficients from Kato-type classes

@article{Liskevich2009HarnackIA, title={Harnack inequality and continuity of solutions to quasi-linear degenerate parabolic equations with coefficients from Kato-type classes}, author={Vitali Liskevich and Igor I. Skrypnik}, journal={Journal of Differential Equations}, year={2009}, volume={247}, pages={2740-2777} }

## 24 Citations

### Continuity of solutions to singular parabolic equations with coefficients from Kato-type classes

- Mathematics
- 2016

We prove local boundedness and continuity of solutions to divergence type quasi-linear singular parabolic equations with measurable coefficients and lower order terms from nonlinear Kato classes.

### Removable singularities of quasilinear parabolic equations with coefficients from Kato-type classes

- Mathematics
- 2015

We establish the best possible condition for point singularities to be removable for nonlinear parabolic equations in divergent form with lower-order terms from the nonlinear Kato classes.

### Gradient estimates for degenerate quasi‐linear parabolic equations

- MathematicsJ. Lond. Math. Soc.
- 2011

For a general class of divergence type quasi-linear degenerate parabolic equations with differentiable structure and lower order coefficients form bounded with respect to the Laplacian, estimates are obtained for the gradients of solutions and it is shown that the solutions are Lipschitz continuous withrespect to the space variable.

### Pointwise estimates for solutions of singular quasi-linear parabolic equations

- Mathematics
- 2012

For a class of singular divergence type quasi-linear parabolicequations with a Radon measure on the right hand side we derivepointwise estimates for solutions via the nonlinear Wolffpotentials.

### Potential Estimates for Quasi-Linear Parabolic Equations

- Mathematics
- 2010

Abstract For a class of divergence type quasi-linear degenerate parabolic equations with a Radon measure on the right hand side we derive pointwise estimates for solutions via nonlinear Wolff…

### Holder regularity of solutions of generalized p-Laplacian type parabolic equations

- Mathematics
- 2012

Using ideas from the theory of Orlicz spaces, we discuss the Holder regularity of a bounded weak solution of a p−Laplacian type parabolic partial differential equation under generalized structure…

### Green matrices and continuity of the weak solutions for the elliptic systems with lower order terms

- Mathematics
- 2016

In this paper, we consider the second-order elliptic systems with lower order terms coefficients belonging to Kato–Stummel type classes in a bounded domain Ω ⊆ ℝn, where n ≥ 3. We establish the…

### Local subestimates of solutions to double-phase parabolic equations via nonlinear parabolic potentials

- MathematicsJournal of Mathematical Sciences
- 2019

For parabolic equations with nonstandard growth conditions, we prove local boundedness of weak solutions in terms of nonlinear parabolic potentials of the right-hand side of the equation.

### Global existence and blowup for quasilinear parabolic equations not in divergence form

- Mathematics
- 2013

### Pointwise estimates of solutions to the double-phase elliptic equations

- Mathematics
- 2017

With the help of nonlinear Wolf potentials, we derive the pointwise estimates for the weak solutions to inhomogeneous quasilinear double-phase elliptic equations of the divergence type.

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