Equivalence of viscosity and weak solutions for a p-parabolic equation

被引：7
|
作者：
Siltakoski, Jarkko [1 ]
机构：
[1] Univ Jyvaskyla, Dept Math & Stat, POB 35, Jyvaskyla 40014, Finland
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2021年 / 21卷 / 02期
关键词：
Comparison principle; Gradient term; Parabolic p-Laplacian; Viscosity solution; Weak solution; SUPERSOLUTIONS; REGULARITY; BOUNDARY; MAXIMUM;
D O I：
10.1007/s00028-020-00666-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the relationship of viscosity and weak solutions to the equation partial derivative(t)u - Delta(p)u = f (Du), where p > 1 and f is an element of C(R-N) satisfies suitable assumptions. Our main result is that bounded viscosity supersolutions coincide with bounded lower semicontinuous weak supersolutions. Moreover, we prove the lower semicontinuity of weak supersolutions when p >= 2.
引用
收藏
页码：2047 / 2080
页数：34
相关论文
共 50 条
  • [11] Equivalence of viscosity and weak solutions for the normalized p(x)-Laplacian
    Jarkko Siltakoski
    Calculus of Variations and Partial Differential Equations, 2018, 57
  • [12] p-parabolic Approximation of Total Variation Flow Solutions
    Gianazza, Ugo
    Klaus, Colin
    INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2019, 68 (05) : 1519 - 1550
  • [13] The tusk condition and Petrovskii criterion for the normalized p-parabolic equation
    Bjorn, Anders
    Bjorn, Jana
    Parviainen, Mikko
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2019, 100 (02): : 623 - 643
  • [14] Equivalence of weak and viscosity solutions to the p(x)-Laplacian in Carnot groups
    Bieske, Thomas
    Freeman, Robert D.
    ANALYSIS AND MATHEMATICAL PHYSICS, 2019, 9 (04) : 1583 - 1610
  • [15] Characterizations of interior polar sets for the degenerate p-parabolic equation
    Avelin, Benny
    Saari, Olli
    JOURNAL OF EVOLUTION EQUATIONS, 2017, 17 (02) : 827 - 848
  • [16] Characterizations of interior polar sets for the degenerate p-parabolic equation
    Benny Avelin
    Olli Saari
    Journal of Evolution Equations, 2017, 17 : 827 - 848
  • [17] STRONGLY P-PARABOLIC SYSTEMS
    HASEGAWA, Y
    PROCEEDINGS OF THE JAPAN ACADEMY, 1961, 37 (08): : 473 - &
  • [18] Equivalence and regularity of weak and viscosity solutions for the anisotropic p(<middle dot>)-Laplacian
    Ochoa, Pablo
    Valverde, Federico Ramos
    NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2024, 31 (05):
  • [19] Second order Sobolev regularity results for the generalized p-parabolic equation
    Feng, Yawen
    Parviainen, Mikko
    Sarsa, Saara
    JOURNAL OF FUNCTIONAL ANALYSIS, 2025, 288 (05)
  • [20] Existence and Uniqueness of Weak Solutions to the p-biharmonic Parabolic Equation
    Guo Jin-yong
    Gao Wen-jie
    CommunicationsinMathematicalResearch, 2013, 29 (03) : 261 - 270
12345