An interior second derivative bound for solutions of Hessian equations

John Urbas

doi:10.1007/PL00009920

An interior second derivative bound for solutions of Hessian equations

John Urbas^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

Abstract

In previous work we showed that weak solutions in W^2,p(Ω) of the k-Hessian equation F_k[u] = g(cursive chi) have locally bounded second derivatives if g is positive and sufficiently smooth and p > kn/2. Here we improve this result to p > k(n - 1)/2, which is known to be sharp in the Monge-Ampère case k = n > 2.

Original language	English
Pages (from-to)	417-431
Number of pages	15
Journal	Calculus of Variations and Partial Differential Equations
Volume	12
Issue number	4
DOIs	https://doi.org/10.1007/PL00009920
Publication status	Published - Jun 2001

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title = "An interior second derivative bound for solutions of Hessian equations",

abstract = "In previous work we showed that weak solutions in W2,p(Ω) of the k-Hessian equation Fk[u] = g(cursive chi) have locally bounded second derivatives if g is positive and sufficiently smooth and p > kn/2. Here we improve this result to p > k(n - 1)/2, which is known to be sharp in the Monge-Amp{\`e}re case k = n > 2.",

author = "John Urbas",

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N2 - In previous work we showed that weak solutions in W2,p(Ω) of the k-Hessian equation Fk[u] = g(cursive chi) have locally bounded second derivatives if g is positive and sufficiently smooth and p > kn/2. Here we improve this result to p > k(n - 1)/2, which is known to be sharp in the Monge-Ampère case k = n > 2.

AB - In previous work we showed that weak solutions in W2,p(Ω) of the k-Hessian equation Fk[u] = g(cursive chi) have locally bounded second derivatives if g is positive and sufficiently smooth and p > kn/2. Here we improve this result to p > k(n - 1)/2, which is known to be sharp in the Monge-Ampère case k = n > 2.

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U2 - 10.1007/PL00009920

DO - 10.1007/PL00009920

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EP - 431

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 4

ER -

An interior second derivative bound for solutions of Hessian equations

Abstract

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