Regularity for double-phase functionals with nearly linear growth and two modulating coefficients

초록

We deal with non-uniformly elliptic integral functionals wbar right arrow integral[c(x)divided by Dw divided by log(1+divided by Dw divided by)+a(x)(divided by Dw divided by(2)+s(2))(q/2)+1]dx, with s is an element of [0,1] , q>1 , 0 <= c(.)<=Lambda,a(.)>= 0 , and a(x)+c(x)>= 1/Lambda for some Lambda>0 . In this article, we establish that the gradient of a local minimizer for the aforementioned functionals is locally Holder continuous.

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