Counterexamples to maximal regularity for operators in divergence form Article Swipe

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Sebastian Bechtel , Connor Mooney , Mark Veraar ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.1007/s00013-024-02014-9

In this paper, we present counterexamples to maximal $$L^p$$ -regularity for a parabolic PDE. The example is a second-order operator in divergence form with space and time-dependent coefficients. It is well-known from Lions’ theory that such operators admit maximal $$L^2$$ -regularity on $$H^{-1}$$ under a coercivity condition on the coefficients, and without any regularity conditions in time and space. We show that in general one cannot expect maximal $$L^p$$ -regularity on $$H^{-1}(\mathbb {R}^d)$$ or $$L^2$$ -regularity on $$L^2(\mathbb {R}^d)$$ .

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Mathematics Counterexample Divergence (linguistics) Pure mathematics Discrete mathematics Combinatorics Philosophy Linguistics

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Type: article
Language: en
Landing Page: https://doi.org/10.1007/s00013-024-02014-9
PDF: https://link.springer.com/content/pdf/10.1007/s00013-024-02014-9.pdf
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Cited By: 4
References: 16
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DOI: https://doi.org/10.1007/s00013-024-02014-9

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Title: Counterexamples to maximal regularity for operators in divergence form

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Language: en

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Publication year: 2024

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Publication date: 2024-06-20

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Authors: Sebastian Bechtel, Connor Mooney, Mark Veraar

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Landing page: https://doi.org/10.1007/s00013-024-02014-9

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Concepts: Mathematics, Counterexample, Divergence (linguistics), Pure mathematics, Discrete mathematics, Combinatorics, Philosophy, Linguistics

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Cited by: 4

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