On the Preservation of Eccentricities of Monge–Ampère Sections

Maldonado, Diego

doi:10.1007/978-3-319-30961-3_12

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Sections Of Solutions To Monge-ampère Equations1

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2019

2021

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Cited by 2 publications

(2 citation statements)

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“…We finish this section by stating a lemma (inspired by Maldonado [8]) which confirms that dilated sections are well-separated.…”

Section: Sections Of Solutions To Monge-ampère Equationsmentioning

confidence: 79%

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An interior a priori estimate for solutions to Monge-Ampère equations with right-hand side close to a positive constant

O'Neill

Cheng

2021

Journal of Differential Equations

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“…We finish this section by stating a lemma (inspired by Maldonado [8]) which confirms that dilated sections are well-separated.…”

Section: Sections Of Solutions To Monge-ampère Equationsmentioning

confidence: 79%

“…In other words, we may use them in a similar way that Euclidean balls are used for estimates of the Poisson equation (see, for example, [5]). We then give a proof of our main result in Section 3, using techniques from [7] and also using results inspired by [8] concerning shrinking sections of Monge-Ampère solutions.…”

mentioning

confidence: 99%

An interior a priori estimate for solutions to Monge-Ampère equations with right-hand side close to a positive constant

O'Neill

Cheng

2021

Journal of Differential Equations

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An Interior A Priori Estimate for Solutions to Monge-Ampère Equations with Right-Hand Side Close to One

O’Neill¹,

Cheng²

2019

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We consider Monge-Ampére equations with the right hand side function close to a constant and from a function class that is larger than any Hölder 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.

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On the Preservation of Eccentricities of Monge–Ampère Sections

Cited by 2 publications

References 21 publications

An interior a priori estimate for solutions to Monge-Ampère equations with right-hand side close to a positive constant

An interior a priori estimate for solutions to Monge-Ampère equations with right-hand side close to a positive constant

An Interior A Priori Estimate for Solutions to Monge-Ampère Equations with Right-Hand Side Close to One

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