Zobrazeno 1 - 10
of 191
pro vyhledávání: '"Bögelein, Verena"'
We study the local regularity properties of $(s,p)$-harmonic functions, i.e. local weak solutions to the fractional $p$-Laplace equation of order $s\in (0,1)$ in the case $p\in (1,2]$. It is shown that $(s,p)$-harmonic functions are weakly differenti
Externí odkaz:
http://arxiv.org/abs/2409.02012
Higher Sobolev and H\"older regularity is studied for local weak solutions of the fractional $p$-Laplace equation of order $s$ in the case $p\ge 2$. Depending on the regime considered, i.e. $$0
Externí odkaz:
http://arxiv.org/abs/2406.01568
This paper is devoted to studying the local behavior of non-negative weak solutions to the doubly non-linear parabolic equation \begin{equation*} \partial_t u^q - \text{div}\big(|D u|^{p-2}D u\big) = 0 \end{equation*} in a space-time cylinder. H\"old
Externí odkaz:
http://arxiv.org/abs/2305.08539
In a cylindrical space-time domain with a convex, spatial base, we establish a local Lipschitz estimate for weak solutions to parabolic systems with Uhlenbeck structure up to the lateral boundary, provided homogeneous Dirichlet data are assumed on th
Externí odkaz:
http://arxiv.org/abs/2110.09407
We demonstrate two proofs for the local H\"older continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is \[ \partial_t\big(|u|^{q-1}u\big)-\Delta_p u=0,\quad p>2,\quad 0
Externí odkaz:
http://arxiv.org/abs/2108.02749
We establish the interior and boundary H\"older continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is \[ \partial_t\big(|u|^{p-2}u\big)-\Delta_p u=0,\quad p>1. \] The proof relies on the
Externí odkaz:
http://arxiv.org/abs/2003.04158
In this article we establish the existence of weak solutions to the shallow medium equation. We proceed by an approximation argument. First we truncate the coefficients of the equation from above and below. Then we prove convergence of the solutions
Externí odkaz:
http://arxiv.org/abs/2001.07942
In this paper we establish in the fast diffusion range the higher integrability of the spatial gradient of weak solutions to porous medium systems. The result comes along with an explicit reverse H\"older inequality for the gradient. The novel featur
Externí odkaz:
http://arxiv.org/abs/1811.09241
This paper proves a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The new feature of the argument is that the intrinsic geometry involves the solution as well as its spatial gradie
Externí odkaz:
http://arxiv.org/abs/1810.06039