Local subestimates of solutions to double-phase parabolic equations via nonlinear parabolic potentials

被引:0
作者
Buryachenko K.O. [1 ]
机构
[1] Kateryna Oleksandrivna Buryachenko Vasyl’ Stus Donetsk National University, Vinnytsia
关键词
Double-phase parabolic equations; local boundedness; local subestimetes; parabolic potentials; weak solutions;
D O I
10.1007/s10958-019-04515-3
中图分类号
学科分类号
摘要
For parabolic equations with nonstandard growth conditions, we prove local boundedness of weak solutions in terms of nonlinear parabolic potentials of the right-hand side of the equation. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
引用
收藏
页码:772 / 786
页数:14
相关论文
共 24 条
  • [11] Kilpelainen T., Maly J., The Wiener test and potential estimates for quasilinear elliptic equations, Acta Math., 172, 1, pp. 137-161, (1994)
  • [12] Kuusi T., Mingione G., Riesz potentials and non-linear parabolic equations, ARMA, 212, pp. 727-780, (2014)
  • [13] Ladyzhenskaya O.A., Solonnikov V.A., Ural'Tseva N.N., Linear and Quasilinear Equations of Parabolic Type, (1967)
  • [14] Lieberman G.M., The natural generalizationj of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations, Communications in Partial Differential Equations, 16, 2-3, pp. 311-361, (1991)
  • [15] Liskevich V., Skrypnik I.I., Harnack inequality and continuity of solutions to quasi-linear degenerate parabolic equations with coefficients from Kato-type classes, Journal of Differential Equations, 247, 10, pp. 2740-2777, (2009)
  • [16] Liskevich V., Skrypnik I.I., Sobol Z., Estimates of solutions for the parabolic $p$-Laplacian equation with measure via parabolic nonlinear potentials, Communications on Pure and Applied Analysis, 12, 4, pp. 1731-1744, (2012)
  • [17] Liskevich V., Skrypnik I.I., Poitwise estimates for solutions to the porous medium equation with measure as a forcing term, Israel J. Math., 194, pp. 259-275, (2013)
  • [18] Marcellini P., Regularity of minimizers of integrals of the calculus of variations with non standard growth conditions, Arch. Rat. Mech. Analys., 105, 3, pp. 267-284, (1989)
  • [19] Marcellini P., Regularity and existence of solutions of elliptic equations with (p
  • [20] q)-growth conditions, J. Diff. Equa., 90, 1, pp. 1-30, (1991)