# 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

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topBildhauer, 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 < \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 < \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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