Open Access
Volume 29, 2023
Article Number 2
Number of page(s) 35
Published online 11 January 2023
  1. K. Adimurthi, H. Prasad and V. Tewary, Local Holder regularity for nonlocal parabolic p-Laplace equations. arXiv:2205.09695 [math] (2022). [Google Scholar]
  2. V. Bögelein, F. Duzaar and P. Marcellini, Parabolic systems with p, q-growth: a variational approach. Arch. Ratl. Mech. Anal. 210 (2013) 219–267. [CrossRef] [Google Scholar]
  3. V. Bögelein, F. Duzaar and P. Marcellini, Existence of evolutionary variational solutions via the calculus of variations. J. Differ. Equ. 256 (2014) 3912–3942. [CrossRef] [Google Scholar]
  4. V. Bögelein, F. Duzaar, P. Marcellini and S. Signoriello, Nonlocal diffusion equations. J. Math. Anal. Appl. 432 (2015) 398–428. [CrossRef] [MathSciNet] [Google Scholar]
  5. V. Bögelein, F. Duzaar, L. Schötzler and C. Scheven, Existence for evolutionary problems with linear growth by stability methods. J. Differ. Equ. 266 (2019) 7709–7748. [CrossRef] [Google Scholar]
  6. L. Brasco and E. Lindgren, Higher Sobolev regularity for the fractional p-Laplace equation in the superquadratic case. Adv. Math. 304 (2017) 300–354. [CrossRef] [MathSciNet] [Google Scholar]
  7. L. Brasco, E. Lindgren and E. Parini, The fractional Cheeger problem. Interf. Free Bound. 16 (2014) 419–458. [CrossRef] [Google Scholar]
  8. L. Brasco, E. Lindgren and A. Schikorra, Higher Hölder regularity for the fractional p-Laplacian in the superquadratic case. Adv. Math. 338 (2018) 782–846. [CrossRef] [MathSciNet] [Google Scholar]
  9. L. Brasco, E. Lindgren and M. Stroömqvist, Continuity of solutions to a nonlinear fractional diffusion equation. J. Evolut. Equ. 4 (2021) 4319–4381. [CrossRef] [Google Scholar]
  10. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York (2011). [Google Scholar]
  11. S.-S. Byun, J. Ok and K. Song, Hölder regularity for weak solutions to nonlocal double phase problems. arXiv:2108.09623 [math] (2021). [Google Scholar]
  12. L. Caffarelli, C.H. Chan and A. Vasseur, Regularity theory for parabolic nonlinear integral operators. J. Am. Math. Soc. 24 (2011) 849–869. [CrossRef] [Google Scholar]
  13. L. Caffarelli and A. Vasseur, Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Ann. Math. Sec. Ser. 171 (2010) 1903–1930. [CrossRef] [Google Scholar]
  14. J. Chaker, Regularity of solutions to anisotropic nonlocal equations. Math. Zeitsch. 296 (2020) 1135–1155. [CrossRef] [Google Scholar]
  15. J. Chaker and M. Kassmann, Nonlocal operators with singular anisotropic kernels. Commun. Partial Differ. Equ. 45 (2020) 1–31. [CrossRef] [Google Scholar]
  16. J. Chaker and M. Kim, Local regularity for nonlocal equations with variable exponents. arXiv:2107.06043 [math] (2021). [Google Scholar]
  17. J. Chaker and M. Kim, Regularity estimates for fractional orthotropic p-Laplacians of mixed order. Adv. Nonlinear Anal. 11 (2022) 1307–1331. [CrossRef] [MathSciNet] [Google Scholar]
  18. J. Chaker, M. Kim and M. Weidner, Regularity for nonlocal problems with non-standard growth. arXiv:2111.09182 [math] (2021). [Google Scholar]
  19. H. Chang-Lara and G. Dávila, Regularity for solutions of nonlocal parabolic equations II. J. Differ. Equ. 256 (2014) 130–156. [CrossRef] [Google Scholar]
  20. M. Cozzi, Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: a unified approach via fractional De Giorgi classes. J. Funct. Anal. 272 (2017) 4762–4837. [CrossRef] [MathSciNet] [Google Scholar]
  21. E. De Giorgi, Conjectures concerning some evolution problems. Duke Math. J. 81 (1996) 255–268. [CrossRef] [MathSciNet] [Google Scholar]
  22. A. Di Castro, T. Kuusi and G. Palatucci, Local behavior of fractional p-minimizers. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 33 (2016) 1279–1299. [CrossRef] [MathSciNet] [Google Scholar]
  23. E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136 (2012) 521–573. [Google Scholar]
  24. I. Fonseca, N. Fusco and P. Marcellini, An existence result for a nonconvex variational problem via regularity. ESAIM: COCV 7 (2002) 69–95. [CrossRef] [EDP Sciences] [Google Scholar]
  25. S. Ghosh, D. Kumar, H. Prasad and V. Tewary, Existence of variational solutions to doubly nonlinear nonlocal evolution equations via minimizing movements. J. Evol. Equ. 22 (2022) 74. [CrossRef] [Google Scholar]
  26. Q. Han, Compact Sobolev-Slobodeckij embeddings and positive solutions to fractional Laplacian equations. Adv. Nonlinear Anal. 11 (2022) 432–453. [Google Scholar]
  27. J. Kinnunen and P. Lindqvist, Pointwise behaviour of semicontinuous supersolutions to a quasilinear parabolic equation. Ann. Matem. Pura Appl. 185 (2006) 411–435. [CrossRef] [Google Scholar]
  28. J. Kinnunen and M. Masson, Parabolic comparison principle and quasiminimizers in metric measure spaces. Proc. Am. Math. Soc. 143 (2015) 621–632. [Google Scholar]
  29. T. Kuusi, G. Mingione and Y. Sire, Nonlocal self-improving properties. Anal. PDE 8 (2015) 57–114. [CrossRef] [MathSciNet] [Google Scholar]
  30. H.C. Lara and G. Dávila, Regularity for solutions of non local parabolic equations. Calc. Variat. Partial Differ. Equ. 49 (2014) 139–172. [CrossRef] [Google Scholar]
  31. N. Liao, Höolder regularity for parabolic fractional p-Laplacian, arXiv:2205.10111 [math] (2022). [Google Scholar]
  32. A. Lichnewsky and R. Temam, Pseudosolutions of the time-dependent minimal surface problem. J. Differ. Equ. 30 (1978) 340–364. [CrossRef] [Google Scholar]
  33. P. Marcellini, Regularity of minimizers of integrals of the calculus of variations with nonstandard growth conditions. Arch. Ratl. Mech. Anal. 105 (1989) 267–284. [CrossRef] [Google Scholar]
  34. P. Marcellini, Regularity and existence of solutions of elliptic equations with p,q-growth conditions. J. Differ. Equ. 90 (1991) 1-30. [CrossRef] [Google Scholar]
  35. P. Marcellini, Regularity for elliptic equations with general growth conditions. J. Differ. Equ. 105 (1993) 296–333. [CrossRef] [Google Scholar]
  36. P. Marcellini, Regularity for some scalar variational problems under general growth conditions. J. Optim. Theory Appl. 90 (1996) 161–181. [CrossRef] [MathSciNet] [Google Scholar]
  37. P. Marcellini, Regularity under general and p, q– growth conditions. Discr. Continu. Dyn. Syst. S 13 (2020) 2009. [Google Scholar]
  38. A. Menovschikov, A. Molchanova and L. Scarpa, An extended variational theory for nonlinear evolution equations via modular spaces. SIAM J. Math. Anal. 53 (2021) 4865–4907. [CrossRef] [MathSciNet] [Google Scholar]
  39. G. Mingione and V. Radulescu, Recent developments in problems with nonstandard growth and nonuniform ellipticity. J. Math. Anal. Appl. 1 (2021) 125-197. [Google Scholar]
  40. M. Parviainen, Global higher integrability for parabolic quasiminimizers in nonsmooth domains. Calc. Variat. Partial Differ. Equ. 31 (2008) 75–98. [Google Scholar]
  41. H. Prasad and V. Tewary, Local boundedness of variational solutions to nonlocal double phase parabolic equations. arXiv:2112.02345 [math] (2021). [Google Scholar]
  42. F. Rindler, Calculus of Variations. Universitext. Springer, Cham (2018). [CrossRef] [Google Scholar]
  43. L. Scarpa and U. Stefanelli, Stochastic PDEs via convex minimization. Commun. Partial Differ. Equ. 46 (2021) 66–97. [CrossRef] [Google Scholar]
  44. J.M. Scott and T. Mengesha, Self-Improving inequalities for bounded weak solutions to nonlocal double phase equations. Commun. Pure Appl. Anal. 21 (2022) 183. [MathSciNet] [Google Scholar]
  45. E. Serra and P. Tilli, Nonlinear wave equations as limits of convex minimization problems: proof of a conjecture by De Giorgi. Ann. Math. Second Ser. 175 (2012) 1551–1574. [CrossRef] [Google Scholar]
  46. R.E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, volume 49 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (1997). [Google Scholar]
  47. U. Stefanelli, The De Giorgi conjecture on elliptic regularization. Math. Models Methods Appl. Sci. 21 (2011) 1377–1394. [Google Scholar]
  48. M. Strömqvist, Local boundedness of solutions to non-local parabolic equations modeled on the fractional p-Laplacian. J. Differ. Equ. 266 (2019) 7948–7979. [CrossRef] [Google Scholar]
  49. W. Wieser, Parabolic Q-minima and minimal solutions to variational flow. Manuscr. Math. 59 (1987) 63–107. [CrossRef] [Google Scholar]

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