LP REGULARITY OF VELOCITY AVERAGES

被引：153

作者：

DIPERNA, RJ ^{[1
]}

LIONS, PL ^{[1
]}

MEYER, Y ^{[1
]}

机构：

[1] UNIV PARIS 09,CEREMADE,PL DE-LATTRE-DE-TASSIGNY,F-75576 PARIS 16,FRANCE

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 1991年 / 8卷 / 3-4期

关键词：

VELOCITY AVERAGES; SOBOLEV AND BESOV SPACES; TRANSPORT EQUATIONS; LP MULTIPLIERS;

D O I：

10.1016/S0294-1449(16)30264-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we present some general regularity results for "velocity averages" i.e. averages in v of functions f(x, v) for which (v. NABLA (x)f) has some given regularity. We are able to cover general regularity classes for both f and (v. NABLA (x)f) and we thus extend various known results. Our methods of proof rely on Littlewood-Paley type decompositions, interpolation arguments and a spectral decomposition adapted to the "velocity direction".

引用

页码：271 / 287

页数：17

共 20 条

[1]

Agoshkov V.I., 1984, SOV MATH DOKL, V29, P662

[2]

AGOSHKOV VI, FUNCTIONAL SPACES H1

[3]

Bergh J., 1976, INTERPOLATION SPACES, V223

[4] SOME RECENT DEVELOPMENTS IN FOURIER-ANALYSIS AND HP-THEORY ON PRODUCT DOMAINS [J].

CHANG, SYA ;

FEFFERMAN, R .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1985, 12 (01) :1-43

[5]

CHANG SYA, 1982, AM J MATH, V104, P445

[6]

DESVILLETTES L, COMMUNICATION

[7]

DIPERNA R, 1988, CR ACAD SCI I-MATH, V307, P655

[8]

DIPERNA R, 1988, CR ACAD SCI I-MATH, V306, P343

[9] ON THE CAUCHY-PROBLEM FOR BOLTZMANN EQUATIONS - GLOBAL EXISTENCE AND WEAK STABILITY [J].

DIPERNA, RJ ;

LIONS, PL .

ANNALS OF MATHEMATICS, 1989, 130 (02) :321-366

[10]

DIPERNA RJ, 1990, IN PRESS SEMINARIO M

← 1 2 →