An Interior A Priori Estimate for Solutions to Monge-Amp\`ere Equations with Right-Hand Side Close to One
| Autor: | O'Neill, Thomas, Cheng, Bin |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We consider Monge-Amp\'ere equations with the right hand side function close to a constant and from a function class that is larger than any H\"older 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. Comment: 14 pages |
| Databáze: | arXiv |
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