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A general notion of
uniform ellipticity and the regularity of the stress field
for elliptic equations in divergence form
Umberto Guarnotta and Sunra Mosconi |
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Vol. 16 (2023), No. 8, 1955–1988
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Abstract |
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For solutions of we show that the quasiconformality of is the key property leading to the Sobolev regularity of the stress field , in relation with the summability of . This class of nonlinearities encodes in a general way the notion of uniform ellipticity and encompasses all known instances where the stress field is known to be Sobolev regular. We provide examples showing the optimality of this assumption and present two applications: a nonlinear Cordes condition for equations in divergence form and some partial results on the conjecture. |
Keywords
elliptic equations in divergence form, regularity,
quasiconformal maps, Calderón–Zygmund estimates, Cordes
condition
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Mathematical Subject Classification
Primary: 30C65, 35B65, 35J62
Secondary: 49K20
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Milestones
Received: 21 June 2021
Revised: 18 January 2022
Accepted: 7 March 2022
Published: 16 October 2023
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Authors |
| Umberto Guarnotta | |
| Dipartimento di Matematica e
Informatica Università degli Studi di Catania Catania Italy |
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| Sunra Mosconi | |
| Dipartimento di Matematica e
Informatica Università degli Studi di Catania Catania Italy |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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