Geodesic
A regularity theory for scalar local minimizers of splitting-type variational integrals
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 3, pp. 385-404

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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.

Classification : 49N60 
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     author = {Bildhauer, Michael and Fuchs, Martin and Zhong, Xiao},
     title = {A regularity theory for scalar local minimizers of splitting-type variational integrals},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {385--404},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 6},
     number = {3},
     year = {2007},
     mrnumber = {2370266},
     zbl = {1150.49015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_3_385_0/}
}
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Bildhauer, Michael; Fuchs, Martin; Zhong, Xiao. A regularity theory for scalar local minimizers of splitting-type variational integrals. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 3, pp. 385-404. http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_3_385_0/