Random homogenization of fractional obstacle problems

Previous Article
Duality results in the homogenization of two-dimensional high-contrast conductivities
NHM Home
This Issue
Next Article
Direct integral decomposition for periodic function spaces and application to Bloch waves

September 2008, 3(3): 523-554. doi: 10.3934/nhm.2008.3.523

Random homogenization of fractional obstacle problems

Luis Caffarelli ^1, and Antoine Mellet ^2,

1.	Department of Mathematics, University of Texas at Austin, 1 University Station, C1200, Austin, TX 78712-1082, United States
2.	Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada

Received January 2008 Published March 2008

Abstract
Related Papers

We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.

Keywords: Obstacle Problem, Homogenization, Fractional Laplace.

Mathematics Subject Classification: Primary: 74Q05; Secondary: 35R3.

Citation: Luis Caffarelli, Antoine Mellet. Random homogenization of fractional obstacle problems. Networks & Heterogeneous Media, 2008, 3 (3) : 523-554. doi: 10.3934/nhm.2008.3.523

[1]	Fahd Jarad, Thabet Abdeljawad. Generalized fractional derivatives and Laplace transform. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 709-722. doi: 10.3934/dcdss.2020039
[2]	Ali Fuat Alkaya, Dindar Oz. An optimal algorithm for the obstacle neutralization problem. Journal of Industrial & Management Optimization, 2017, 13 (2) : 835-856. doi: 10.3934/jimo.2016049
[3]	Fanghua Lin, Xiaodong Yan. A type of homogenization problem. Discrete & Continuous Dynamical Systems - A, 2003, 9 (1) : 1-30. doi: 10.3934/dcds.2003.9.1
[4]	Juan J. Manfredi, Julio D. Rossi, Stephanie J. Somersille. An obstacle problem for Tug-of-War games. Communications on Pure & Applied Analysis, 2015, 14 (1) : 217-228. doi: 10.3934/cpaa.2015.14.217
[5]	Takeshi Fukao, Masahiro Kubo. Time-dependent obstacle problem in thermohydraulics. Conference Publications, 2009, 2009 (Special) : 240-249. doi: 10.3934/proc.2009.2009.240
[6]	Walter Allegretto, Yanping Lin, Shuqing Ma. Hölder continuous solutions of an obstacle thermistor problem. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 983-997. doi: 10.3934/dcdsb.2004.4.983
[7]	Song Wang. Numerical solution of an obstacle problem with interval coefficients. Numerical Algebra, Control & Optimization, 2019, 0 (0) : 0-0. doi: 10.3934/naco.2019030
[8]	Renata Bunoiu, Claudia Timofte. Homogenization of a thermal problem with flux jump. Networks & Heterogeneous Media, 2016, 11 (4) : 545-562. doi: 10.3934/nhm.2016009
[9]	Sunghan Kim, Ki-Ahm Lee, Henrik Shahgholian. Homogenization of the boundary value for the Dirichlet problem. Discrete & Continuous Dynamical Systems - A, 2019, 0 (0) : 1-22. doi: 10.3934/dcds.2019234
[10]	Jinggang Tan, Jingang Xiong. A Harnack inequality for fractional Laplace equations with lower order terms. Discrete & Continuous Dynamical Systems - A, 2011, 31 (3) : 975-983. doi: 10.3934/dcds.2011.31.975
[11]	Claudia Bucur. Some observations on the Green function for the ball in the fractional Laplace framework. Communications on Pure & Applied Analysis, 2016, 15 (2) : 657-699. doi: 10.3934/cpaa.2016.15.657
[12]	Amir Khan, Asaf Khan, Tahir Khan, Gul Zaman. Extension of triple Laplace transform for solving fractional differential equations. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 755-768. doi: 10.3934/dcdss.2020042
[13]	Salvatore A. Marano, Sunra J. N. Mosconi. Some recent results on the Dirichlet problem for $(p, q)$-Laplace equations. Discrete & Continuous Dynamical Systems - S, 2018, 11 (2) : 279-291. doi: 10.3934/dcdss.2018015
[14]	John C. Schotland, Vadim A. Markel. Fourier-Laplace structure of the inverse scattering problem for the radiative transport equation. Inverse Problems & Imaging, 2007, 1 (1) : 181-188. doi: 10.3934/ipi.2007.1.181
[15]	Ben Schweizer, Marco Veneroni. The needle problem approach to non-periodic homogenization. Networks & Heterogeneous Media, 2011, 6 (4) : 755-781. doi: 10.3934/nhm.2011.6.755
[16]	Brian Sleeman. The inverse acoustic obstacle scattering problem and its interior dual. Inverse Problems & Imaging, 2009, 3 (2) : 211-229. doi: 10.3934/ipi.2009.3.211
[17]	Laurent Denis, Anis Matoussi, Jing Zhang. The obstacle problem for quasilinear stochastic PDEs with non-homogeneous operator. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5185-5202. doi: 10.3934/dcds.2015.35.5185
[18]	Fabio Camilli, Paola Loreti, Naoki Yamada. Systems of convex Hamilton-Jacobi equations with implicit obstacles and the obstacle problem. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1291-1302. doi: 10.3934/cpaa.2009.8.1291
[19]	José-Francisco Rodrigues, João Lita da Silva. On a unilateral reaction-diffusion system and a nonlocal evolution obstacle problem. Communications on Pure & Applied Analysis, 2004, 3 (1) : 85-95. doi: 10.3934/cpaa.2004.3.85
[20]	J.I. Díaz, D. Gómez-Castro. Steiner symmetrization for concave semilinear elliptic and parabolic equations and the obstacle problem. Conference Publications, 2015, 2015 (special) : 379-386. doi: 10.3934/proc.2015.0379

2018 Impact Factor: 0.871

American Institute of Mathematical Sciences