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Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations

Abstract:
We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal positive number, (ii) the solutions are very close to a single standard bubble in a universal positive distance around each blow-up point, and (iii) the heights of these bubbles are comparable by a universal factor. As an application of this result, we establish a quantitative Liouville theorem.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00526-017-1192-y

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Institution:
University of Oxford
Oxford college:
St Edmund Hall
Role:
Author
Publisher:
Springer Verlag Publisher's website
Journal:
Calculus of Variations and Partial Differential Equations Journal website
Volume:
56
Pages:
99
Publication date:
2017-06-19
Acceptance date:
2017-05-04
DOI:
EISSN:
1432-0835
ISSN:
0944-2669
Source identifiers:
692399
Pubs id:
pubs:692399
UUID:
uuid:26a62566-e56c-4010-99c2-2bfaeeb7a5b2
Local pid:
pubs:692399
Deposit date:
2017-05-05

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