Mean value properties of solutions of linear partial differential equations

被引：0

作者：

Meshkov V.Z. ^{[1
]}

Polovinkin I.P. ^{[1
]}

机构：

[1] Voronezh State University, Voronezh

来源：

Journal of Mathematical Sciences | 2009年 / 160卷 / 1期

关键词：

Harmonic Function; Elliptic Equation; Regular Solution; Hyperbolic Equation; Helmholtz Equation;

D O I：

10.1007/s10958-009-9483-2

中图分类号：

学科分类号：

摘要：

The present paper suggests a uniform viewpoint to mean value theorems for linear elliptic and hyperbolic partial differential equations that, in a certain cases, allows one to obtain new mean value formulas. Also, the authors consider a method for obtaining mean value formulas for elliptic equations from those for hyperbolic equations. © 2009 Springer Science+Business Media, Inc.

引用

页码：45 / 52

页数：7

共 50 条

[1] Mean value theorems for solutions of linear partial differential equations
A. V. Pokrovskii
Mathematical Notes, 1998, 64 : 220 - 229
[2] Mean value theorems for solutions of linear partial differential equations
Pokrovskii, AV
MATHEMATICAL NOTES, 1998, 64 (1-2) : 220 - 229
[3] Mean Value Theorems for Linear Partial Differential Equations
Polovinkin I.P.
Journal of Mathematical Sciences, 2014, 197 (3) : 399 - 403
[4] Disoscillability of solutions to partial differential equations on manifolds of constant curvature and mean value theorems
M. K. Bugir
Siberian Mathematical Journal, 1997, 38 : 871 - 880
[5] Disoscillability of solutions to partial differential equations on manifolds of constant curvature and mean value theorems
Bugir, MK
SIBERIAN MATHEMATICAL JOURNAL, 1997, 38 (05) : 871 - 880
[6] POLYNOMIAL SOLUTIONS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS
Petropoulou, Eugenia N.
Siafarikas, Panayiotis D.
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (03) : 1053 - 1065
[7] ANALYTIC SOLUTIONS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS
CIUMASU, D
ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI RENDICONTI-CLASSE DI SCIENZE FISICHE-MATEMATICHE & NATURALI, 1973, 53 (1-2): : 18 - 24
[8] Numerical solutions to initial and boundary value problems for linear fractional partial differential equations
Rehman, Mujeeb Ur
Khan, Rahmat Ali
APPLIED MATHEMATICAL MODELLING, 2013, 37 (07) : 5233 - 5244
[9] THE GEOMETRIC PROPERTIES OF SOLUTIONS OF NON-LINEAR SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS
LAVRENTIEV, MA
SHABAT, BV
DOKLADY AKADEMII NAUK SSSR, 1957, 112 (05): : 810 - 811
[10] The Bolzano mean-value theorem and partial differential equations
Kryszewski, Wojciech
Siemianowski, Jakub
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 457 (02) : 1452 - 1477

← 1 2 3 4 5 →