Boundedness of the hessian of a biharmonic function in a convex domain

Svitlana Mayboroda; Vladimir Maz'ya

doi:10.1080/03605300801891919

Boundedness of the hessian of a biharmonic function in a convex domain

Svitlana Mayboroda, Vladimir Maz'ya

School of Mathematics

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

8 Scopus citations

Abstract

We consider the Dirichlet problem for the biharmonic equation on an arbitrary convex domain and prove that the second derivatives of the variational solution are bounded in all dimensions.

Original language	English (US)
Pages (from-to)	1439-1454
Number of pages	16
Journal	Communications in Partial Differential Equations
Volume	33
Issue number	8
DOIs	https://doi.org/10.1080/03605300801891919
State	Published - Aug 26 2008

Bibliographical note

Funding Information:
The second author Vladimir Maz’ya was partially supported by NSF grant DMS 0500029 and EPSRC grant EP/F005563/1.

Keywords

Biharmonic equation
Convex domain
Dirichlet problem

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10.1080/03605300801891919

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title = "Boundedness of the hessian of a biharmonic function in a convex domain",

abstract = "We consider the Dirichlet problem for the biharmonic equation on an arbitrary convex domain and prove that the second derivatives of the variational solution are bounded in all dimensions.",

keywords = "Biharmonic equation, Convex domain, Dirichlet problem",

author = "Svitlana Mayboroda and Vladimir Maz'ya",

note = "Funding Information: The second author Vladimir Maz{\textquoteright}ya was partially supported by NSF grant DMS 0500029 and EPSRC grant EP/F005563/1.",

year = "2008",

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doi = "10.1080/03605300801891919",

language = "English (US)",

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T1 - Boundedness of the hessian of a biharmonic function in a convex domain

AU - Mayboroda, Svitlana

AU - Maz'ya, Vladimir

N1 - Funding Information: The second author Vladimir Maz’ya was partially supported by NSF grant DMS 0500029 and EPSRC grant EP/F005563/1.

PY - 2008/8/26

Y1 - 2008/8/26

N2 - We consider the Dirichlet problem for the biharmonic equation on an arbitrary convex domain and prove that the second derivatives of the variational solution are bounded in all dimensions.

AB - We consider the Dirichlet problem for the biharmonic equation on an arbitrary convex domain and prove that the second derivatives of the variational solution are bounded in all dimensions.

KW - Biharmonic equation

KW - Convex domain

KW - Dirichlet problem

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DO - 10.1080/03605300801891919

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AN - SCOPUS:49549123386

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JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 8

ER -

Boundedness of the hessian of a biharmonic function in a convex domain

Abstract

Bibliographical note

Keywords

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