Free Access
Issue
ESAIM: COCV
Volume 27, 2021
Article Number 19
Number of page(s) 26
DOI https://doi.org/10.1051/cocv/2021017
Published online 22 March 2021
  1. C. Benassi and M. Caselli, Lipschitz continuity results for obstacle problems. Rendiconti Lincei, Matematica e Applicazioni 31 (2020) 191–210. [Google Scholar]
  2. L. Beck and G. Mingione, Lipschitz bounds and nonuniform ellipticity. Commun. Pure Appl. Math. 73 (2020) 944–1034. [Google Scholar]
  3. V. Bögelein, F. Duzaar and P. Marcellini, Parabolic systems with p, q-growth: a variational approach. Arch. Ration. Mech. Anal. 210 (2013) 219–267. [Google Scholar]
  4. L. Caffarelli, The regularity of elliptic and parabolic free boundaries. Bull. Am. Math. Soc. 82 (1976) 616–618. [Google Scholar]
  5. L.A. Caffarelli and A. Figalli, Regularity of solutions to the parabolic fractional obstacle problem. J. Reine Angew. Math. 680 (2013) 191–233. [Google Scholar]
  6. M. Carozza, J. Kristensen and A. Passarelli di Napoli, Regularity of minimizers of autonomous convex variational integrals. Ann. Sc. Norm. Super. Pisa Cl. Sci. XIII (2014) 1065–1089. [Google Scholar]
  7. M. Carozza, J. Kristensen and A. Passarelli di Napoli, On the validity of the Euler Lagrange system. Commun. Pure Appl. Anal. 14 (2018) 51–62. [Google Scholar]
  8. M. Caselli, A. Gentile and R. Giova, Regularity results for solutions to obstacle problems with Sobolev coefficients. J. Diff. Equ. 269 (2020) 8308–8330. [Google Scholar]
  9. I. Chlebicka and C. De Filippis, Removable sets in non-uniformly elliptic problems. Annali Mat. Pura Appl. 199 (2020) 619–649. . [Google Scholar]
  10. M. Colombo and G. Mingione, Regularity for double phase variational problems. Arch. Rat. Mech. Anal. 215 (2015) 443–496. [Google Scholar]
  11. G. Cupini, F. Giannetti, R. Giova and A. Passarelli di Napoli, Regularity results for vectorial minimizers of a class of degenerate convex integrals. J. Diff. Equ. 265 (2018) 4375–4416. [Google Scholar]
  12. G. Cupini, M. Guidorzi and E. Mascolo, Regularity of minimizers of vectorial integrals with pq growth. Nonlinear Anal. 54 (2003) 591–616. [Google Scholar]
  13. G. Cupini, P. Marcellini and E. Mascolo, Local boundedness of solutions to quasilinear elliptic systems. Manuscr. Math. 137 (2012) 287–315. [Google Scholar]
  14. G. Cupini, P. Marcellini and E. Mascolo, Local boundedness of solutions to some anisotropic elliptic systems. Contemp. Math. 595 (2013) 169–186. [Google Scholar]
  15. G. Cupini, P. Marcellini and E. Mascolo, Local boundedness of minimizers with limit growth conditions. J. Optim. Theory Appl. 166 (2015) 1–22. [Google Scholar]
  16. C. De Filippis, Regularity results for a class of non-autonomous obstacle problems with (p, q)-growth. To appear J. Math. Anal. Appl. doi.org/10.1016/j.jmaa.2019.123450 (2019). [PubMed] [Google Scholar]
  17. C. De Filippis and G. Mingione, On the regularity of minima of non-autonomous functionals. J. Geom. Anal. 30 (2020) 1661–1723. [Google Scholar]
  18. C. De Filippis and G. Mingione, Lipschitz bounds and non autonomous integrals. Preprint arxiv.org/abs/2007.07469 (2020). [Google Scholar]
  19. C. De Filippis and G. Palatucci, Hölder regularity for nonlocal double phase equations. J. Diff. Equ. 267 (2018) 547–586. [Google Scholar]
  20. M. Eleuteri, P. Marcellini and E. Mascolo, Lipschitz estimates for systems with ellipticity conditions at infinity. Ann. Mat. Pura e Appl. 195 (2016) 1575–1603. [Google Scholar]
  21. M. Eleuteri, P. Marcellini and E. Mascolo, Lipschitz continuity for energy integrals with variable exponents. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 27 (2016) 61–87. [Google Scholar]
  22. M. Eleuteri, P. Marcellini and E. Mascolo, Regularity for scalar integrals without structure conditions. Adv. Calc. Var. 13 (2020) 279–300. [Google Scholar]
  23. M. Eleuteri and A. Passarelli di Napoli, Higher differentiability for solutions to a class of obstacle problems. Calc. Var. Partial Differ. Equ. 57 (2018) 115. [Google Scholar]
  24. M. Eleuteri and A. Passarelli di Napoli, Regularity results for a class of non-differentiable obstacle problems. Nonlinear Anal. 194 (2020) 111434. [Google Scholar]
  25. A. Figalli, B. Krummel and X. Ros-Oton, On the regularity of the free boundary in the p-Laplacian obstacle problem. J. Differ. Equ. 263 (2017) 1931–1945. [Google Scholar]
  26. M. Fuchs, Variational inequalities for vector valued functions with non convex obstacles. Analysis 5 (1985) 223–238. [Google Scholar]
  27. M. Fuchs and G. Mingione, Full regularity for free and constrained local minimizers of elliptic variational integrals with nearly linear growth. Manuscripta Math. 102 (2000) 227–250. [CrossRef] [Google Scholar]
  28. C. Gavioli, Higher differentiability for a class of obstacle problems with nonstandard growth conditions. Forum Matematicum 31 (2019) 1501–1516. [Google Scholar]
  29. R. Giova, Higher differentiability for n-harmonic systems with Sobolev coefficients. J. Differ. Equ. 259 (2015) 5667–5687. [Google Scholar]
  30. R. Giova and A. Passarelli di Napoli, Regularity results for a priori bounded minimizers of non-autonomous functionals with discontinuous coefficients. Adv. Calc. Var. 12 (2019) 85–110. [Google Scholar]
  31. E. Giusti, Direct methods in the calculus of variations. World Scientific Publishing Co. (2003). [Google Scholar]
  32. P. Hariulehto and P. Hästö, Double phase image restoration. J. Math. Anal. Appl. 2020 (2020) 123832. [Google Scholar]
  33. J. Hirschand M. Schäffner, Growth conditions and regularity, an optimal local boundedness result. Commun. Contemp. Math. 2020 (2020) 2050029. [Google Scholar]
  34. P. Marcellini, Un example de solution discontinue d’un problème variationnel dans le cas scalaire. Preprint 11, Istituto Matematico “U. Dini”, Università di Firenze (1987). [Google Scholar]
  35. P. Marcellini, Regularity of minimizers of integrals of the calculus of variations with nonstandard growth conditions. Arch. Ration. Mech. Anal. 105 (1989) 267–284. [Google Scholar]
  36. P. Marcellini, Regularity and existence of solutions of elliptic equations with p, q-growth conditions. J. Differ. Equ. 90 (1991) 1–30. [Google Scholar]
  37. P. Marcellini, Regularity for elliptic equations with general growth conditions. J. Differ. Equ. 105 (1993) 296–333. [Google Scholar]
  38. P. Marcellini, A variational approach to parabolic equations under general and p, q-growth conditions. Nonlinear Anal. (2019), DOI 10.1016/j.na.2019.02.010. [Google Scholar]
  39. A. Passarelli di Napoli, Higher differentiability of minimizers of variational integrals with Sobolev coefficients. Adv. Calc. Var. 7 (2014) 59–89. [Google Scholar]
  40. A. Passarelli di Napoli, Higher differentiability of solutions of elliptic systems with Sobolev coefficients: the case p = n = 2. Pot. Anal. 41 (2014) 715–735. [Google Scholar]
  41. A. Passarelli di Napoli, Regularity results for non-autonomous variational integrals with discontinuous coefficients. Atti Accad. Naz. Lincei, Rend. Lincei Mat. Appl. 26 (2015) 475–496. [Google Scholar]
  42. A. Petrosyan, H. Shahgholian and N. Uraltseva, Regularity of Free Boundaries in Obstacle-Type Problems. Graduate Studies in Mathematics. American Mathematical Society (2012). [Google Scholar]
  43. M.A. Ragusa and A. Tachikawa, Regularity for minimizers for functionals of double phase with variable exponents. Adv. Nonlinear Anal. 9 (2019) 710–728. [Google Scholar]

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