We consider degenerate and singular parabolic equations with p-Laplacian structure in bounded nonsmooth domains when the right-hand side is a signed Radon measure finite total mass. develop new tool that allows global regularity estimates for spatial gradient of solutions to such data problems, by introducing (intrinsic) fractional maximal function given measure.

In this paper we prove some existence and regularity results concerning parabolic equations ut = F (x,∇u, D u) + f(x, t) with some boundary conditions, on Ω×]0, T [, where Ω is some bounded domain which possesses the exterior cone property and F is some fully nonlinear elliptic operator, singular or degenerate.

We consider the Dirichlet problem for a class of elliptic and parabolic equations in upper-half space $\mathbb{R}^d_+$, where coefficients are product $x_d^\alpha, \alpha \in (-\infty, 1),$ bounded uniformly matrix coefficients. Thus, singular or degenerate near boundary $\{x_d =0\}$ they may not locally integrable. The novelty work is that we find proper weights under which existence, uniquene...

<p style='text-indent:20px;'>The aim of this paper is to prove existence and regularity solutions for the following nonlinear singular parabolic problem</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \left\{ \begin{array}{lll} \dfrac{\partial u}{\partial t}-\mbox{div}\left( \dfrac{a(x,t,u,\nabla u)}{(1+|u|)^{\the...

<p style='text-indent:20px;'>In this paper we study the boundary controllability for a system of two coupled degenerate/singular parabolic equations with control acting on only one equation. We analyze both approximate and null properties. Besides, provide an estimate null-control cost. The proofs are based detailed spectral analysis use moment method by Fattorini Russell together some re...

This paper is addressed to establishing controllability and observability for some forward linear stochastic complex degenerate/singular Ginzburg-Landau equations. It sufficient establish appropriate inequalities the corresponding backward The key prove Carleman estimates of operators. Compared with existing deterministic results, it necessary overcome difficulties caused by coefficients random...