C1,α regularity for the normalized p-Poisson problem

被引：35

作者：

Attouchi, Amal ^{[1
]}

Parviainen, Mikko ^{[1
]}

Ruosteenoja, Eero ^{[1
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, POB 35, Jyvaskyla 40014, Finland

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2017年 / 108卷 / 04期

基金：

芬兰科学院;

关键词：

Normalized p-Laplacian; p-Poisson problem; Viscosity solutions; Local C-1; C-alpha regularity; TUG-OF-WAR; VISCOSITY SOLUTIONS; WEAK SOLUTIONS; EQUIVALENCE; LAPLACIAN; EQUATION; PROOF;

D O I：

10.1016/j.matpur.2017.05.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the normalized p-Poisson problem Delta(N)(p)u = f in Omega subset of R-n. The normalized p -Laplacian Delta(N)(p)u := vertical bar Du vertical bar(2-P)Delta(p)u is in non -divergence form and arises for example from stochastic games. We prove C-loc(1-alpha) regularity with nearly optimal alpha for viscosity solutions of this problem. In the case f is an element of L-infinity boolean AND C and p > 1 we use methods both from viscosity and weak theory, whereas in the case f is an element of L-q boolean AND C, q > max(n, E/2, 2), and p > 2 we rely on the tools of nonlinear potential theory. (C) 2017 Elsevier Masson SAS. All rights reserved.

引用

页码：553 / 591

页数：39

共 50 条

[21] C1,1 regularity for solutions to the degenerate Lp Dual Minkowski problem
Chen, Li
Tu, Qiang
Wu, Di
Xiang, Ni
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2021, 60 (03)
[22] Differentiability of potential energies with a parameter and shape sensitivity analysis for nonlinear case: the p-Poisson problem
K. Ohtsuka
M. Kimura
Japan Journal of Industrial and Applied Mathematics, 2012, 29 : 23 - 35
[23] Differentiability of potential energies with a parameter and shape sensitivity analysis for nonlinear case: the p-Poisson problem
Ohtsuka, K.
Kimura, M.
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2012, 29 (01) : 23 - 35
[24] Sharp inequalities connected to the homogenized p-Poisson equation
Lukkassen, D
MATHEMATICAL INEQUALITIES & APPLICATIONS, 1999, 2 (02): : 243 - 250
[25] C1,a regularity of interfaces for solutions of the parabolic p-Laplacian equation
Ko, Y
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1999, 24 (5-6) : 915 - 950
[26] The asymptotic p-Poisson equation as p → ∞in Carnot-Caratheodory spaces
Capogna, Luca
Giovannardi, Gianmarco
Pinamonti, Andrea
Verzellesi, Simone
MATHEMATISCHE ANNALEN, 2024, 390 (02) : 2113 - 2153
[27] Boundary regularity estimates for nonlocal elliptic equations in C1 and C1,α domains
Ros-Oton, Xavier
Serra, Joaquim
ANNALI DI MATEMATICA PURA ED APPLICATA, 2017, 196 (05) : 1637 - 1668
[28] C1,α-regularity for p-harmonic functions in the Heisenberg group for p near 2
Domokos, A
Manfredi, JJ
p-Harmonic Equation and Recent Advances in Analysis, 2005, 370 : 17 - 23
[29] Menger curvature and C1 regularity of fractals
Lin, Y
Mattila, P
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (06) : 1755 - 1762
[30] C1,1 Regularity for Solutions to the Degenerate Dual Orlicz-Minkowski Problem
Wu, Di
ACTA MATHEMATICA SCIENTIA, 2025, 45 (02) : 327 - 337

← 1 2 3 4 5 →