The self-improving property of higher integrability in the obstacle problem for the porous medium equation

Cho, Yumi; Scheven, Christoph

doi:10.1007/s00030-019-0581-7

Cited by 4 publications

(2 citation statements)

References 34 publications

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“…In summary, there are some differences between these two approaches and the second approach has more advantages. Recently, Cho and Scheven [5,6] proved the higher integrability of weak solutions to obstacle problems related to the porous medium equation and their proofs followed the approach in [1,2]. In [6] the authors used the boundary term (1.5) to establish an energy estimate and a gluing lemma for weak solutions of the obstacle problem.…”

Section: Introductionmentioning

confidence: 99%

“…To this end, the present work is intended as an attempt to follow the approach in [10] to establish a self-improving result for the obstacle problem. In this paper, we shall use the intrinsic cylinder of the type (1.2) and we will not make any use of boundary term (1.5) which is a basic tool in [1,2,5,6]. The result of this paper was first announced in [15].…”

Section: Introductionmentioning

confidence: 99%

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Higher integrability for obstacle problem related to the singular porous medium equation

2020

Bound Value Probl

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In this paper we study the self-improving property of the obstacle problem related to the singular porous medium equation by using the method developed by Gianazza and Schwarzacher (J. Funct. Anal. 277(12):1–57, 2019). We establish a local higher integrability result for the spatial gradient of the mth power of nonnegative weak solutions, under some suitable regularity assumptions on the obstacle function. In comparison to the work by Cho and Scheven (J. Math. Anal. Appl. 491(2):1–44, 2020), our approach provides some new aspects in the estimations of the nonnegative weak solution of the obstacle problem.

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