2020
DOI: 10.48550/arxiv.2011.03944
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Regularity of weak supersolutions to elliptic and parabolic equations: lower semicontinuity and pointwise behavior

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Cited by 3 publications
(10 citation statements)
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“…• Lower and upper semicontinuity of weak supersolutions and subsolutions, respectively (Theorem 9.2 and Corollary 9.3). This result is an adaptation to the mixed local and nonlocal case of a measure theoretic approach (Lemma 9.1) in Liao [27]. We refer to Banerjee-Garain-Kinnunen [2] for an adaptation of this approach to a class of doubly nonlinear parabolic nonlocal problems.…”
Section: Introductionmentioning
confidence: 90%
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“…• Lower and upper semicontinuity of weak supersolutions and subsolutions, respectively (Theorem 9.2 and Corollary 9.3). This result is an adaptation to the mixed local and nonlocal case of a measure theoretic approach (Lemma 9.1) in Liao [27]. We refer to Banerjee-Garain-Kinnunen [2] for an adaptation of this approach to a class of doubly nonlinear parabolic nonlocal problems.…”
Section: Introductionmentioning
confidence: 90%
“…Before stating our results on pointwise behavior, we discuss a result from Liao [27]. Let u be a measurable function that is locally essentially bounded below in Ω.…”
Section: Semicontinuitymentioning
confidence: 99%
“…Our final result asserts that the lower semicontinuous representative u * , given by Theorem 5.1, is determined by previous times. The proof follows by a combination of Lemma 5.7 below and the proof of [35,Theorem 3.1].…”
Section: Semicontinuity and Pointwise Behavior Of Subsolutions And Su...mentioning
confidence: 99%
“…Local boundedness, Harnack inequalities, Hölder continuity among several other regularity results are discussed in DiBenedetto [19] and DiBenedetto-Gianazza-Vespri [20]. For lower semicontinuity and further properties of weak supersolutions, we refer to Kinnunen-Lindqvist [33], Kuusi [34], Liao [35] and the references therein. In the purely nonlocal case b = 0, existence, uniqueness and asymptotic behavior of strong solutions of (1.7) were studied by Mazón-Rossi-Toledo [37] and Vázquez [40].…”
Section: ˆRnmentioning
confidence: 99%
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