Regularity for general functionals with double phase

@article{Baroni2017RegularityFG,
  title={Regularity for general functionals with double phase},
  author={P. Baroni and Maria Colombo and G. Mingione},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2017},
  volume={57},
  pages={1-48}
}
We prove sharp regularity results for a general class of functionals of the type $$\begin{aligned} w \mapsto \int F(x, w, Dw) \, dx, \end{aligned}$$w↦∫F(x,w,Dw)dx,featuring non-standard growth conditions and non-uniform ellipticity properties. The model case is given by the double phase integral $$\begin{aligned} w \mapsto \int b(x,w)(|Dw|^p+a(x)|Dw|^q) \, dx,\quad 1<p < q, \quad a(x)\ge 0, \end{aligned}$$w↦∫b(x,w)(|Dw|p+a(x)|Dw|q)dx,1<p<q,a(x)≥0,with $$0<\nu \le b(\cdot )\le L $$0<ν≤b(·)≤L… Expand
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