Some interior regularity results for solutions of Hessian equations

John Urbas

doi:10.1007/s005260050001

Some interior regularity results for solutions of Hessian equations

John Urbas^*

^*Corresponding author for this work

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

23 Citations (Scopus)

Abstract

We prove monotonicity formulae related to degenerate k-Hessian equations which yield Morrey type estimates for certain integrands involving the second derivatives of the solution. In the special case k = 2 we deduce that weak solutions in W^2,p(Ω), p > n - 1, have locally Hölder continuous gradients. In the nondegenerate case we also show that weak solutions in W^2,p(Ω), p > kn/2, have locally bounded second derivatives.

Original language	English
Pages (from-to)	1-31
Number of pages	31
Journal	Calculus of Variations and Partial Differential Equations
Volume	11
Issue number	1
DOIs	https://doi.org/10.1007/s005260050001
Publication status	Published - Aug 2000

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title = "Some interior regularity results for solutions of Hessian equations",

abstract = "We prove monotonicity formulae related to degenerate k-Hessian equations which yield Morrey type estimates for certain integrands involving the second derivatives of the solution. In the special case k = 2 we deduce that weak solutions in W2,p(Ω), p > n - 1, have locally H{\"o}lder continuous gradients. In the nondegenerate case we also show that weak solutions in W2,p(Ω), p > kn/2, have locally bounded second derivatives.",

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N2 - We prove monotonicity formulae related to degenerate k-Hessian equations which yield Morrey type estimates for certain integrands involving the second derivatives of the solution. In the special case k = 2 we deduce that weak solutions in W2,p(Ω), p > n - 1, have locally Hölder continuous gradients. In the nondegenerate case we also show that weak solutions in W2,p(Ω), p > kn/2, have locally bounded second derivatives.

AB - We prove monotonicity formulae related to degenerate k-Hessian equations which yield Morrey type estimates for certain integrands involving the second derivatives of the solution. In the special case k = 2 we deduce that weak solutions in W2,p(Ω), p > n - 1, have locally Hölder continuous gradients. In the nondegenerate case we also show that weak solutions in W2,p(Ω), p > kn/2, have locally bounded second derivatives.

UR - https://www.scopus.com/pages/publications/0013090015

U2 - 10.1007/s005260050001

DO - 10.1007/s005260050001

M3 - Article

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SP - 1

EP - 31

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 1

ER -

Some interior regularity results for solutions of Hessian equations

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