Zobrazeno 1 - 10
of 18
pro vyhledávání: '"Lehtelä, Pekka"'
We deal with the obstacle problem for the porous medium equation in the slow diffusion regime $m>1$. Our main interest is to treat fairly irregular obstacles assuming only boundedness and lower semicontinuity. In particular, the considered obstacles
Externí odkaz:
http://arxiv.org/abs/1807.07810
We study the relations between different regularity assumptions in the definition of weak solutions and supersolutions to the porous medium equation. In particular, we establish the equivalence of the conditions $u^m \in L^2_{\rm loc}(0,T;H^1_{\rm lo
Externí odkaz:
http://arxiv.org/abs/1801.05249
In the slow diffusion case unbounded supersolutions of the porous medium equation are of two totally different types, depending on whether the pressure is locally integrable or not. This criterion and its consequences are discussed.
Externí odkaz:
http://arxiv.org/abs/1801.04121
Autor:
Lehtelä, Pekka
In this work, we prove a weak Harnack estimate for the weak supersolutions to the porous medium equation. The proof is based on a priori estimates for the supersolutions and measure theoretical arguments.
Externí odkaz:
http://arxiv.org/abs/1607.00785
Autor:
Lehtelä, Pekka, Lukkari, Teemu
We prove that various notions of supersolutions to the porous medium equation are equivalent under suitable conditions. More spesifically, we consider weak supersolutions, very weak supersolutions, and $m$-superporous functions defined via a comparis
Externí odkaz:
http://arxiv.org/abs/1603.03641
This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincar\'e inequality. Such a functional is defined through relaxation, and it defines a Radon measure on the space
Externí odkaz:
http://arxiv.org/abs/1401.5717
Publikováno v:
In Journal of Differential Equations 5 February 2019 266(4):1851-1864
Publikováno v:
Analysis and Geometry in Metric Spaces, Vol 4, Iss 1 (2016)
This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincaré inequality. Such a functional is defined via relaxation, and it defines a Radon measure on the space. For
Externí odkaz:
https://doaj.org/article/a419b179231f4377813f55a0500b88fd
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