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Comparison principles and Lipschitz regularity for some nonlinear degenerate elliptic equations

Abstract:
We establish interior Lipschitz regularity for continuous viscosity solutions of fully nonlinear, conformally invariant, degenerate elliptic equations. As a by-product of our method, we also prove a weak form of the strong comparison principle, which we refer to as the principle of propagation of touching points, for operators of the form ∇2ψ + L(x, ψ, ∇ψ) which are non-decreasing in ψ.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1007/s00526-018-1369-z

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
St Edmund Hall
Role:
Author
Publisher:
Springer Berlin Heidelberg Publisher's website
Journal:
Calculus of Variations and Partial Differential Equations Journal website
Volume:
57
Issue:
4
Pages:
Article: 96
Publication date:
2018-06-11
Acceptance date:
2018-05-12
DOI:
EISSN:
1432-0835
ISSN:
0944-2669
Pubs id:
pubs:847690
URN:
uri:fe6a4084-1163-4892-b39b-60a2a104c69e
UUID:
uuid:fe6a4084-1163-4892-b39b-60a2a104c69e
Local pid:
pubs:847690

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