Venttsel' problems in fractal domains

被引：24
作者：
Lancia, Maria Rosaria [1 ]
Vernole, Paola [2 ]
机构：
[1] Univ Rome, Dipartimento Sci Base & Applicate Ingn, Via A Scarpa 16, I-00161 Rome, Italy
[2] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2014年 / 14卷 / 03期
关键词：
Asymptotic behaviour; Venttsel' problems; Energy forms; Fractal domains; Trace theorems; Semigroups; Varying Hilbert spaces; BOUNDARY-CONDITIONS; APPROXIMATION; TRANSMISSION; CONVERGENCE; SPACES; LAPLACIAN;
D O I：
10.1007/s00028-014-0233-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A nonsteady Venttsel' problem in a fractal domain Omega or in the corresponding prefractal domain Omega (h) is studied. Existence, uniqueness, and regularity results for the strict solution, in both cases, are established as well as convergence results of the solutions of the approximating problems in varying Hilbert spaces.
引用
收藏
页码：681 / 712
页数：32
相关论文
共 62 条
[51]  
Lions J.L, 1968, Problemes Aux Limites Non Homogenes
[52]  
Lions J. L., 1696, PROBLEMES LIMITES NO, V2
[53]  
LUNARDI A., 1995, PROGR NONLINEAR DIFF, V16
[54]   COMPOSITE MEDIA AND ASYMPTOTIC DIRICHLET FORMS [J].
MOSCO, U .
JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 123 (02) :368-421
[55]   CONVERGENCE OF CONVEX SETS AND OF SOLUTIONS OF VARIATIONAL INEQUALITIES [J].
MOSCO, U .
ADVANCES IN MATHEMATICS, 1969, 3 (04) :510-&
[56]  
Mosco U., 2003, REND ACCAD NAZ SCI 4, V27, P237
[57]  
NECAS J, 1967, METHODES DIRECTES TH
[58]  
Pazy A., 1993, SEMIGROUPS LINEAR OP, DOI DOI 10.1007/978-1-4612-5561-1
[59]   GENERAL FORMULATION OF LAPLACIAN TRANSFER ACROSS IRREGULAR SURFACES [J].
SAPOVAL, B .
PHYSICAL REVIEW LETTERS, 1994, 73 (24) :3314-3316
[60]  
SHINBROT M, 1980, J I MATH APPL, V25, P367
1234567