Extension problem and fractional operators: semigroups and wave equations

被引：0
作者：
José E. Galé
Pedro J. Miana
Pablo Raúl Stinga
机构：
[1] Universidad de Zaragoza,Departamento de Matemáticas e I. U. M. A.
[2] The University of Texas at Austin,Department of Mathematics
来源：
Journal of Evolution Equations | 2013年 / 13卷
关键词：
Primary 35C15; 35K05; 35L05; 47D06; 47D09; 47D62; Secondary 35R01; 35R03; 35J10; 35J70; 46J15; 46N20; 47A52; 26A33; Extension problem; Fractional operator; Dirichlet-to-Neumann map; Heat equation; Wave equation; Operator semigroup; Integrated families;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We extend results of Caffarelli–Silvestre and Stinga–Torrea regarding a characterization of fractional powers of differential operators via an extension problem. Our results apply to generators of integrated families of operators, in particular to infinitesimal generators of bounded C0 semigroups and operators with purely imaginary symbol. We give integral representations to the extension problem in terms of solutions to the heat equation and the wave equation.
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页码：343 / 368
页数：25
相关论文
共 41 条
[1]  
Arendt W.(1987)Vector-valued Laplace transform and Cauchy problems Israel J. Math. 59 327-352
[2]  
Caffarelli L.(2008)Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian Invent. Math. 171 425-461
[3]  
Salsa S.(2007)An extension problem related to the fractional Laplacian Comm. Partial Differential Equations 32 1245-1260
[4]  
Silvestre L.(2010)Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation Ann. of Math. (2) 171 1903-1930
[5]  
Caffarelli L.(2002)Gaussian estimates and J. Evol. Equ. 2 299-317
[6]  
Silvestre L.(2011)-boundedness of Riesz means Math. 226 1410-1432
[7]  
Caffarelli L.(1995)Fractional Laplacian in conformal geometry. Adv J. London Math. Soc. 52 177-184
[8]  
Vasseur A.(1995) spectral independency and J. Funct. Anal. 132 141-169
[9]  
Carron G.(1996) analyticity Proc. Amer. Math. Soc. 124 1445-1458
[10]  
Coulhon T.(2006)Uniformly elliptic operators with measurable coefficients J. Funct. Anal. 237 1-53
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