On Mean Value formulas for solutions to second order linear PDEs

被引：0

作者：

Cupini, Giovanni ^{[1
]}

Lanconelli, Ermanno ^{[1
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, Piazza Porta S Donato 5, I-40126 Bologna, Italy

来源：

ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE | 2021年 / 22卷 / 02期

关键词：

HARNACK INEQUALITY; VALUE PROPERTY; PRINCIPLE; EQUATIONS; KERNELS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we give a general proof of Mean Value formulas for solutions to second order linear PDEs, only based on the local properties of their fundamental solution Gamma. Our proof requires a kind of pointwise vanishing integral condition for the intrinsic gradient of Gamma. Combining our Mean Value formulas with a "descent method" due to Kuptsov, we obtain formulas with improved kernels. As an application, we implement our general results to heat operators on stratified Lie groups and to Kolmogorov operators.

引用

页码：777 / 809

页数：33

共 23 条

[1] [Anonymous], 2010, J MATH SCI-U TOKYO
[2] Bonfiglioli A, 2007, SPRINGER MONOGR MATH, P3
[3] Subharmonic functions in sub-Riemannian settings
Bonfiglioli, Andrea
Lanconelli, Ermanno
[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2013, 15 (02) : 387 - 441
[4] HARNACK INEQUALITY FOR SUM OF SQUARES OF VECTOR-FIELDS PLUS A POTENTIAL
CITTI, G
GAROFALO, N
LANCONELLI, E
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1993, 115 (03) : 699 - 734
[5] Representation formulae of solutions of second order elliptic inequalities
D'Ambrosio, Lorenzo
Mitidieri, Enzo
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 178 : 310 - 336
[6] MEAN-VALUE PROPERTIES OF SOLUTIONS TO PARABOLIC EQUATIONS WITH VARIABLE-COEFFICIENTS
FABES, EB
GAROFALO, N
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1987, 121 (02) : 305 - 316
[7] LEVEL SETS OF THE FUNDAMENTAL SOLUTION AND HARNACK INEQUALITY FOR DEGENERATE EQUATIONS OF KOLMOGOROV TYPE
GAROFALO, N
LANCONELLI, E
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 321 (02) : 775 - 792
[8] ASYMPTOTIC-BEHAVIOR OF FUNDAMENTAL-SOLUTIONS AND POTENTIAL-THEORY OF PARABOLIC OPERATORS WITH VARIABLE-COEFFICIENTS
GAROFALO, N
LANCONELLI, E
[J]. MATHEMATISCHE ANNALEN, 1989, 283 (02) : 211 - 239
[9] LEAST ACTION PRINCIPLE, HEAT PROPAGATION AND SUBELLIPTIC ESTIMATES ON CERTAIN NILPOTENT GROUPS
GAVEAU, B
[J]. ACTA MATHEMATICA, 1977, 139 (1-2) : 95 - 153
[10] VOLUME DENSITIES WITH THE MEAN-VALUE PROPERTY FOR HARMONIC-FUNCTIONS
HANSEN, W
NETUKA, I
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 123 (01) : 135 - 140

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