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A Talenti-type comparison theorem for RCD(K, N) spaces and applications

Abstract:

We prove pointwise and L p -gradient comparison results for solutions to elliptic Dirichlet problems defined on open subsets of a (possibly non-smooth) space with positive Ricci curvature (more precisely of an RCD(K, N) metric measure space, with K > 0 and N ∈ (1, ∞)). The obtained Talenti-type comparison is sharp, rigid and stable with respect to L 2/measured-Gromov-Hausdorff topology; moreover it seems new even for smooth Riemannian manifolds. As applications of such Talenti-type comparison...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00526-021-01971-1

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Institution:
University of Oxford
Department:
MATHEMATICAL INSTITUTE
Sub department:
Mathematical Institute
Oxford college:
St Hilda's College
Role:
Author
ORCID:
0000-0002-1932-7148
Publisher:
Springer Nature Publisher's website
Journal:
Calculus of Variations and Partial Differential Equations Journal website
Volume:
60
Issue:
2021
Article number:
157
Publication date:
2021-07-14
Acceptance date:
2021-03-23
DOI:
EISSN:
1432-0835
ISSN:
0944-2669
Language:
English
Keywords:
Pubs id:
1132073
Local pid:
pubs:1132073
Deposit date:
2021-03-23

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