On the Hölder regularity for obstacle problems to porous medium type equations

被引：0
作者：
Kristian Moring
Leah Schätzler
机构：
[1] Aalto University,Department of Mathematics and Systems Analysis
[2] Paris-Lodron-Universität Salzburg,Fachbereich Mathematik
来源：
Journal of Evolution Equations | 2022年 / 22卷
关键词：
Obstacle problem; Porous medium equation; 35B65; 35D30; 35K65; 35K67; 47J20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We show that signed weak solutions to parabolic obstacle problems with porous medium-type structure are locally Hölder continuous, provided that the obstacle is Hölder continuous.
引用
收藏
相关论文
共 34 条
  • [1] Alt H(1983)Quasilinear elliptic-parabolic differential equations Math. Z. 183 311-341
  • [2] Luckhaus S(2017)A comparison principle for the porous medium equation and its consequences Rev. Mat. Iberoam. 33 573-594
  • [3] Avelin B(2018)Boundary regularity for the porous medium equation Arch. Ration. Mech. Anal. 230 493-538
  • [4] Lukkari T(2014)Continuity estimates for porous medium type equations with measure data J. Funct. Anal. 267 3351-3396
  • [5] Björn A(2017)Hölder regularity for degenerate parabolic obstacle problems Ark. Mat. 55 1-39
  • [6] Björn J(2015)The obstacle problem for the porous medium equation Math. Ann. 363 455-499
  • [7] Gianazza U(2020)Hölder regularity for singular parabolic obstacle problems of porous medium type Int. Math. Res. Not. IMRN 6 1671-1717
  • [8] Siljander J(1993)On the regularity of parabolic equations and obstacle problems with quadratic growth nonlinearities J. Differential Equations 102 101-118
  • [9] Bögelein V(1985)Hölder estimates for nonlinear degenerate parabolic systems J. Reine Angew. Math. 357 1-22
  • [10] Duzaar F(2008)Definition and properties of supersolutions to the porous medium equation J. Reine Angew. Math. 618 135-168
1234