Vamsi P. Pingali
Abstract:
We establish
estimates for PDE of the form convex + a sum
of weakly concave functions of the Hessian, thus generalising a recent
result of Collins which is in turn inspired by a theorem of Caffarelli
and Yuan. We apply this result to prove a unique continuation result
for a generalised Monge-Ampere PDE. Independently, we also prove an
existence result for a special case.
Submitted July 15, 2015. Published July 4, 2016.
Math Subject Classifications: 35J60, 35J96.
Key Words: Evans-Krylov-Safonov theory; nonconcave equations;
generalised Monge-Ampere equations.
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Vamsi P. Pingali Department of Mathematics Indian Institute of Science Bangalore, India, 560012 email: vpingali@math.jhu.edu |
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