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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.
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 for
We continue to study regularity results for weak solutions of the large class of second order degenerate quasilinear equations of the form begin{eqnarray} text{div}big(A(x,u, abla u)big) = B(x,u, abla u)text{ for }xinOmega onumber end{eqnarray} as co
We prove matrix and scalar differential Harnack inequalities for linear parabolic equations on Riemannian and Kahler manifolds.
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.
We give a proof of Holder continuity for bounded local weak solutions to the equation $u_t= sum_{i=1}^N (|u_{x_i}|^{p_i-2} u_{x_i})_{x_i}$, in $Omega times [0,T]$, with $Omega subset subset mathbb{R}^N$, under the condition $ 2<p_i<bar{p}(1+2/N)$ f