Generalized Gagliardo-Nirenberg estimates and differentiability of the solutions to monotone nonlinear parabolic systems

被引：7

作者：

Marino, Mario ^{[1
]}

Maugeri, Antonino ^{[1
]}

机构：

[1] Univ Catania, Dept Math & Comp Sci, I-95125 Catania, Italy

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2008年 / 40卷 / 1-3期

关键词：

generalized Sobolev spaces; Gagliardo-Nirenberg estimates; nonlinear parabolic systems; interior differentiability;

D O I：

10.1007/s10898-007-9184-7

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we are concerned with interior differentiability of weak solutions u to nonlinear parabolic systems with natural growth and coefficients uniformly monotone in Du. Making use of estimates of Gagliardo-Nirenberg's type in generalized Sobolev spaces, we show that u belongs to L-2 (-a, 0, H-2 (B(sigma), R-N)) boolean AND H-1 (-a,0,L-2 (B(sigma), R-N)) (see Theorem 3).

引用

页码：185 / 196

页数：12

共 50 条

[21] On one variant of strongly nonlinear Gagliardo-Nirenberg inequality involving Laplace operator with application to nonlinear elliptic problems
Choczewski T.
Kalamajska A.
Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, 2019, 30 (03): : 479 - 496
[22] Differentiability for nonlinear parabolic systems
Marino, M
Maugeri, A
SEVENTH INTERNATIONAL COLLOQUIUM ON DIFFERENTIAL EQUATIONS, PROCEEDINGS, 1997, : 231 - 236
[23] Explicit decay estimates for solutions to nonlinear parabolic systems
Monica Marras
Zeitschrift für angewandte Mathematik und Physik, 2011, 62 : 399 - 404
[24] Explicit decay estimates for solutions to nonlinear parabolic systems
Marras, Monica
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2011, 62 (03): : 399 - 404
[25] A priori estimates for solutions to systems of nonlinear parabolic equations
Belopolskaya Ya.
Journal of Mathematical Sciences, 1998, 92 (6) : 4256 - 4272
[26] Best constants in Sobolev and Gagliardo-Nirenberg inequalities on graded groups and ground states for higher order nonlinear subelliptic equations
Ruzhansky, Michael
Tokmagambetov, Niyaz
Yessirkegenov, Nurgissa
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2020, 59 (05)
[27] Maximum modulus estimates for generalized solutions of doubly nonlinear parabolic equations
Ivanov A.V.
Journal of Mathematical Sciences, 1997, 87 (2) : 3322 - 3342
[28] BOUNDARY ESTIMATES FOR SOLUTIONS OF NONLINEAR DEGENERATE PARABOLIC-SYSTEMS
CHEN, YZ
DIBENEDETTO, E
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1989, 395 : 102 - 131
[29] Lp Estimates for Weak Solutions to Nonlinear Degenerate Parabolic Systems
Wei, Na
Ge, Xiangyu
Wu, Yonghong
Zhao, Leina
DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2017, 2017
[30] Anisotropic Fractional Gagliardo-Nirenberg, Weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type Inequalities, and Applications to Riesz Potentials and p-sub-Laplacian Systems
Aidyn Kassymov
Michael Ruzhansky
Durvudkhan Suragan
Potential Analysis, 2023, 59 : 1971 - 1994

← 1 2 3 4 5 →