Starting from Giaquinta’s counterexample [12] we introduce the class of splitting functionals being of -growth with exponents and show for the scalar case that locally bounded local minimizers are of class . Note that to our knowledge the only -results without imposing a relation between and 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.
@article{ASNSP_2007_5_6_3_385_0, 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://www.numdam.org/item/ASNSP_2007_5_6_3_385_0/} }
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 SP - 385 EP - 404 VL - 6 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2007_5_6_3_385_0/ LA - en ID - ASNSP_2007_5_6_3_385_0 ER -
%0 Journal Article %A Bildhauer, Michael %A Fuchs, Martin %A Zhong, Xiao %T A regularity theory for scalar local minimizers of splitting-type variational integrals %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2007 %P 385-404 %V 6 %N 3 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2007_5_6_3_385_0/ %G en %F ASNSP_2007_5_6_3_385_0
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, Serie 5, Volume 6 (2007) no. 3, pp. 385-404. http://www.numdam.org/item/ASNSP_2007_5_6_3_385_0/
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