19 research outputs found
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 -estimates for the
gradients of solutions, and for the lower order coefficients from a Kato-type
class we show that the solutions are Lipschitz continuous with respect to the
space variable
A note on the weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth
We prove the weak Harnack inequality for the functions which belong to
the corresponding De Giorgi classes under the additional
assumption that with some . In particular, our
result covers new cases of functionals with a variable exponent or double-phase
functionals under the non-logarithmic condition
The impact of intrinsic scaling on the rate of extinction for anisotropic non-Newtonian fast diffusion
We study the decay towards the extinction that pertains to local weak solutions to fully anisotropic equations. Their rates of extinction are evaluated by means of several integral Harnack-type inequalities which constitute the core of our analysis and that are obtained for anisotropic operators having full quasilinear structure. Different decays are obtained when considering different space geometries. The approach is motivated by the research of new methods for strongly nonlinear operators, hence dispensing with comparison principles, while exploiting an intrinsic geometry that affects all the variables of the solution
On the Local Behavior of Local Weak Solutions to some Singular Anisotropic Elliptic Equations
We study the local behavior of bounded local weak solutions to a class of
anisotropic singular equations that involves both non-degenerate and singular
operators. Throughout a parabolic approach to expansion of positivity we obtain
the interior H\"older continuity, and some integral and pointwise Harnack
inequalities.Comment: 32 page