Estimates of solutions for the parabolic $p$-Laplacian equation with measure via parabolic nonlinear potentials

For weak solutions to the evolutional $p$-Laplace equation with a time-dependent Radon measure on the right hand side we obtain pointwise estimates via a nonlinear parabolic potential.

Pointwise estimates for solutions of singular quasi-linear parabolic equations

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

Gradient estimates for degenerate quasi-linear parabolic equations

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 we obtain $L^q$-estimates for the gradients of solutions, and forthe lower order coefficients from a Kato-type class we show that the solutions are Lipschitz continuous with respect to the space variable.

Potential estimates for quasi-linear parabolic equations

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 potentials.

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

For a general class of divergence type quasi-linear degenerate parabolic equations with measurable coeffcients and lower order terms from non-linear Kato-type classes, we prove local boundedness and continuity of solutions, and the intrinsic Harnack inequality for positive solutions.