Regularity of a fourth order nonlinear PDE with critical exponent

Sun Yung A. Chang; Matthew J. Gursky; Paul C. Yang

Regularity of a fourth order nonlinear PDE with critical exponent

Sun Yung A. Chang
, Matthew J. Gursky
, Paul C. Yang

Mathematics

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

49 Scopus citations

Abstract

In this paper we demonstrate the regularity of minimizers for a variational problem, a special case of which arises in spectral theory and conformal geometry. The associated Euler-Lagrange equation is fourth order semilinear; the leading term is the bilaplacian, and lower order terms appear at critical powers.

Original language	English (US)
Pages (from-to)	215-257
Number of pages	43
Journal	American Journal of Mathematics
Volume	121
Issue number	2
State	Published - Apr 1999

All Science Journal Classification (ASJC) codes

General Mathematics

Cite this

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title = "Regularity of a fourth order nonlinear PDE with critical exponent",

abstract = "In this paper we demonstrate the regularity of minimizers for a variational problem, a special case of which arises in spectral theory and conformal geometry. The associated Euler-Lagrange equation is fourth order semilinear; the leading term is the bilaplacian, and lower order terms appear at critical powers.",

author = "Chang, \{Sun Yung A.\} and Gursky, \{Matthew J.\} and Yang, \{Paul C.\}",

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T1 - Regularity of a fourth order nonlinear PDE with critical exponent

AU - Chang, Sun Yung A.

AU - Gursky, Matthew J.

AU - Yang, Paul C.

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N2 - In this paper we demonstrate the regularity of minimizers for a variational problem, a special case of which arises in spectral theory and conformal geometry. The associated Euler-Lagrange equation is fourth order semilinear; the leading term is the bilaplacian, and lower order terms appear at critical powers.

AB - In this paper we demonstrate the regularity of minimizers for a variational problem, a special case of which arises in spectral theory and conformal geometry. The associated Euler-Lagrange equation is fourth order semilinear; the leading term is the bilaplacian, and lower order terms appear at critical powers.

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M3 - Article

AN - SCOPUS:0000453106

SN - 0002-9327

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SP - 215

EP - 257

JO - American Journal of Mathematics

JF - American Journal of Mathematics

IS - 2

ER -

Regularity of a fourth order nonlinear PDE with critical exponent

Abstract

All Science Journal Classification (ASJC) codes

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