Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Moring, Kristian"'
Autor:
Moring, Kristian, Scheven, Christoph
We consider different notions of capacity related to the parabolic $p$-Laplace equation. Our focus is on a variational notion, which is consistent in the full range $1
Externí odkaz:
http://arxiv.org/abs/2409.16066
We prove that bounded weak solutions to degenerate parabolic double-phase equations of $p$-Laplace type are locally H\"older continuous. The proof is based on phase analysis and methods for the $p$-Laplace equation. In particular, the phase analysis
Externí odkaz:
http://arxiv.org/abs/2404.19111
We prove a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems whose prototype is $$ \partial_t \left(|u|^{q-1}u \right) -\operatorname{div} \left( |Du|^{p-2} Du \right) = \operatorname{d
Externí odkaz:
http://arxiv.org/abs/2312.04220
Autor:
Moring, Kristian, Scheven, Christoph
We show that two different notions of solutions to the obstacle problem for the porous medium equation, a potential theoretic notion and a notion based on a variational inequality, coincide for regular enough compactly supported obstacles.
Externí odkaz:
http://arxiv.org/abs/2306.07166
Autor:
Moring, Kristian, Scheven, Christoph
We study a generalized class of supersolutions, so-called supercaloric functions to the porous medium equation in the fast diffusion case. Supercaloric functions are defined as lower semicontinuous functions obeying a parabolic comparison principle.
Externí odkaz:
http://arxiv.org/abs/2306.07155
Autor:
Moring, Kristian, Schätzler, Leah
We show that signed weak solutions to obstacle problems for porous medium type equations with Cauchy-Dirichlet boundary data are continuous up to the parabolic boundary, provided that the obstacle and boundary data are continuous. This result seems t
Externí odkaz:
http://arxiv.org/abs/2306.06009
We prove local higher integrability of the gradient of a weak solution to a degenerate parabolic double-phase system. This result comes with a reverse H\"older type estimate for the gradient. The proof is based on estimates in the intrinsic geometry
Externí odkaz:
http://arxiv.org/abs/2207.06807
Autor:
Moring, Kristian, Schätzler, Leah
We show that signed weak solutions to parabolic obstacle problems with porous medium type structure are locally H\"older continuous, provided that the obstacle is H\"older continuous.
Comment: Typographical errors corrected
Comment: Typographical errors corrected
Externí odkaz:
http://arxiv.org/abs/2202.11565
We study a generalized class of supersolutions, so-called $p$-supercaloric functions, to the parabolic $p$-Laplace equation. This class of functions is defined as lower semicontinuous functions that are finite in a dense set and satisfy the parabolic
Externí odkaz:
http://arxiv.org/abs/2008.12540