A regularity theory for scalar local minimizers of splitting-type variational integrals

Michael Bildhauer; Martin Fuchs; Xiao Zhong

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2007)

  • Volume: 6, Issue: 3, page 385-404
  • ISSN: 0391-173X

Abstract

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Starting from Giaquinta’s counterexample [12] we introduce the class of splitting functionals being of ( p , q ) -growth with exponents p ≤ q < ∞ and show for the scalar case that locally bounded local minimizers are of class C 1 , μ . Note that to our knowledge the only C 1 , μ -results without imposing a relation between p and q concern the case of two independent variables as it is outlined in Marcellini’s paper [15], Theorem A, and later on in the work of Fusco and Sbordone [10], Theorem 4.2.

How to cite

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Bildhauer, Michael, Fuchs, Martin, and Zhong, Xiao. "A regularity theory for scalar local minimizers of splitting-type variational integrals." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 6.3 (2007): 385-404. <http://eudml.org/doc/272272>.

@article{Bildhauer2007,
abstract = {Starting from Giaquinta’s counterexample [12] we introduce the class of splitting functionals being of $(p, q)$-growth with exponents $p \le q &lt; \infty $ and show for the scalar case that locally bounded local minimizers are of class $C^\{1, \mu \}$. Note that to our knowledge the only $C^\{1,\mu \}$-results without imposing a relation between $p$ and $q$ concern the case of two independent variables as it is outlined in Marcellini’s paper [15], Theorem A, and later on in the work of Fusco and Sbordone [10], Theorem 4.2.},
author = {Bildhauer, Michael, Fuchs, Martin, Zhong, Xiao},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {regularity for local minimizers; integral functionals; elliptic conditions},
language = {eng},
number = {3},
pages = {385-404},
publisher = {Scuola Normale Superiore, Pisa},
title = {A regularity theory for scalar local minimizers of splitting-type variational integrals},
url = {http://eudml.org/doc/272272},
volume = {6},
year = {2007},
}

TY - JOUR
AU - Bildhauer, Michael
AU - Fuchs, Martin
AU - Zhong, Xiao
TI - A regularity theory for scalar local minimizers of splitting-type variational integrals
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2007
PB - Scuola Normale Superiore, Pisa
VL - 6
IS - 3
SP - 385
EP - 404
AB - Starting from Giaquinta’s counterexample [12] we introduce the class of splitting functionals being of $(p, q)$-growth with exponents $p \le q &lt; \infty $ and show for the scalar case that locally bounded local minimizers are of class $C^{1, \mu }$. Note that to our knowledge the only $C^{1,\mu }$-results without imposing a relation between $p$ and $q$ concern the case of two independent variables as it is outlined in Marcellini’s paper [15], Theorem A, and later on in the work of Fusco and Sbordone [10], Theorem 4.2.
LA - eng
KW - regularity for local minimizers; integral functionals; elliptic conditions
UR - http://eudml.org/doc/272272
ER -

References

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