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An Interior A Priori Estimate for Solutions to Monge-Amp\`ere Equations with Right-Hand Side Close to One
| Content Provider | Semantic Scholar |
|---|---|
| Author | O'Neill, Thomas A. Cheng, Bin |
| Copyright Year | 2019 |
| Abstract | We consider Monge-Ampere equations with the right hand side function close to a constant and from a function class that is larger than any Holder class and smaller than the Dini-continuous class. We establish an upper bound for the modulus of continuity of the solution's second derivatives. This bound depends exponentially on a quantity similar to but larger than the Dini semi-norm. We establish explicit control on the shape of the sequence of shrinking sections, hence revealing the nature of such exponential dependence. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1911.03120v3.pdf |
| Alternate Webpage(s) | http://arxiv-export-lb.library.cornell.edu/pdf/1911.03120 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
