Regularity results for degenerate elliptic equations related to Gauss measure

被引：0

作者：

Di Blasio, G. ^{[1
]}

Feo, F. ^{[1
]}

Posteraro, M. R. ^{[1
]}

机构：

[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, I-80126 Naples, Italy

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2007年 / 10卷 / 04期

关键词：

Gauss measure; smoothness and regularity of solution of PDE's; elliptic PDE's of degenerate type;

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 study a Dirichlet problem relative to the equation Lu = g phi - (f(i)phi)(xi), where L is a linear elliptic operator with lower-order terms whose ellipticity condition is given in terms of the function phi (x) = (2 pi)(-n/2) exp (-|X|(2)/2), the density of the Gaussian measure. We use the notion of rearrangement with respect to the Gauss measure to obtain a priory estimate of the solution u and we study the summability of u in the Lorentz-Zygmund spaces when g and f(i) varies in suitable Lorent-Zygmund spaces.

引用

页码：771 / 797

页数：27

共 50 条

[31] Holder regularity of solutions of degenerate elliptic and parabolic equations
Daskalopoulos, P
Lee, KA
JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 201 (02) : 341 - 379
[32] Regularity properties of degenerate convolution-elliptic equations
Hummet K Musaev
Veli B Shakhmurov
Boundary Value Problems, 2016
[33] REGULARITY FOR DEGENERATE ELLIPTIC EQUATIONS UNDER MINIMAL ASSUMPTIONS
Borrello, Francesco
MATEMATICHE, 2005, 60 (02): : 397 - 402
[34] Regularity of weak solutions to certain degenerate elliptic equations
Cavalheiro, Albo Carlos
COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2006, 47 (04): : 681 - 693
[35] Regularity properties of degenerate convolution-elliptic equations
Musaev, Hummet K.
Shakhmurov, Veli B.
BOUNDARY VALUE PROBLEMS, 2016, : 1 - 19
[36] Harnack inequality and regularity for degenerate quasilinear elliptic equations
G. Di Fazio
M. S. Fanciullo
P. Zamboni
Mathematische Zeitschrift, 2010, 264 : 679 - 695
[37] Regularity of the solutions of degenerate elliptic equations in divergent form
Amanov, R. A.
Mamedov, F. I.
MATHEMATICAL NOTES, 2008, 83 (1-2) : 3 - 13
[38] Besov regularity for a class of singular or degenerate elliptic equations
Ambrosio, Pasquale
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 505 (02)
[39] Uniform Regularity for Degenerate Elliptic Equations in Perforated Domains
Shen, Zhongwei
Zhuge, Jinping
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2025, 41 (01) : 378 - 412
[40] Regularity for solutions of nonlinear elliptic equations with degenerate coercivity
Benkirane A.
Youssfi A.
Ricerche di Matematica, 2007, 56 (2) : 241 - 275

← 1 2 3 4 5 →