Regularity Results for a Class of Functionals with Non-Standard Growth

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Self-improving property of nonlinear higher order parabolic systems near the boundary (2010, result): “For elliptic regularity results with the standard and also non-standard growth conditions, see for example Acerbi-Mingione [1, 2, 3, 28].”
Boundary regularity of minimizers of p(x)-energy functionals (2016, background): “Let us begin with remembering the following higher integrability results on local minimizers that is originally shown by Zhikov [18] and is generalized by Acerbi and Mingione [1].”
Gradient estimates for the p (x)-Laplacean system (2005, background): “Both conditions have become customary when dealing with the energy (2), see [2], [36].”
Higher integrability for parabolic systems with non-standard growth and degenerate diffusions (2011, background): “[1], [2] for the elliptic case), the C-regularity for degenerate parabolic systems with quasi-diagonal structure, i.”
Overview of differential equations with non-standard growth (2010, methodology): “[27] Acerbi, E.; Mingione, G.: Regularity results for a class of quasiconvex functionals with nonstandard growth.”