November  2008, 7(6): 1295-1333. doi: 10.3934/cpaa.2008.7.1295

The Poisson problem for the exterior derivative operator with Dirichlet boundary condition in nonsmooth domains

1. 

University of Missouri-Columb, Columbia, MO 65211, United States

2. 

University of Missouri-Columbia, Columbia, MO 65211, United States

3. 

Université Aix-Marseille 3, F-13397 Marseille Cédex 20, France

Received  January 2008 Revised  June 2008 Published  August 2008

We formulate and solve the Poisson problem for the exterior derivative operator with Dirichlet boundary condition in Lipschitz domains, of arbitrary topology, for data in Besov and Triebel-Lizorkin spaces.
Citation: Dorina Mitrea, Marius Mitrea, Sylvie Monniaux. The Poisson problem for the exterior derivative operator with Dirichlet boundary condition in nonsmooth domains. Communications on Pure & Applied Analysis, 2008, 7 (6) : 1295-1333. doi: 10.3934/cpaa.2008.7.1295
[1]

Vladimir Georgiev, Koichi Taniguchi. On fractional Leibniz rule for Dirichlet Laplacian in exterior domain. Discrete & Continuous Dynamical Systems - A, 2019, 39 (2) : 1101-1115. doi: 10.3934/dcds.2019046

[2]

Doyoon Kim, Hongjie Dong, Hong Zhang. Neumann problem for non-divergence elliptic and parabolic equations with BMO$_x$ coefficients in weighted Sobolev spaces. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 4895-4914. doi: 10.3934/dcds.2016011

[3]

Aram L. Karakhanyan. Lipschitz continuity of free boundary in the continuous casting problem with divergence form elliptic equation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (1) : 261-277. doi: 10.3934/dcds.2016.36.261

[4]

Shouming Zhou. The Cauchy problem for a generalized $b$-equation with higher-order nonlinearities in critical Besov spaces and weighted $L^p$ spaces. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4967-4986. doi: 10.3934/dcds.2014.34.4967

[5]

Van Duong Dinh. On the Cauchy problem for the nonlinear semi-relativistic equation in Sobolev spaces. Discrete & Continuous Dynamical Systems - A, 2018, 38 (3) : 1127-1143. doi: 10.3934/dcds.2018047

[6]

Dorina Mitrea and Marius Mitrea. Boundary integral methods for harmonic differential forms in Lipschitz domains. Electronic Research Announcements, 1996, 2: 92-97.

[7]

Wolfgang Arendt, Daniel Daners. Varying domains: Stability of the Dirichlet and the Poisson problem. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 21-39. doi: 10.3934/dcds.2008.21.21

[8]

Jongkeun Choi, Hongjie Dong, Doyoon Kim. Conormal derivative problems for stationary Stokes system in Sobolev spaces. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2349-2374. doi: 10.3934/dcds.2018097

[9]

Zhiming Guo, Zhi-Chun Yang, Xingfu Zou. Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition---A non-monotone case. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1825-1838. doi: 10.3934/cpaa.2012.11.1825

[10]

Duchao Liu, Beibei Wang, Peihao Zhao. On the trace regularity results of Musielak-Orlicz-Sobolev spaces in a bounded domain. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1643-1659. doi: 10.3934/cpaa.2016018

[11]

Kazuhiro Ishige, Michinori Ishiwata. Global solutions for a semilinear heat equation in the exterior domain of a compact set. Discrete & Continuous Dynamical Systems - A, 2012, 32 (3) : 847-865. doi: 10.3934/dcds.2012.32.847

[12]

Moez Daoulatli. Energy decay rates for solutions of the wave equation with linear damping in exterior domain. Evolution Equations & Control Theory, 2016, 5 (1) : 37-59. doi: 10.3934/eect.2016.5.37

[13]

Minghua Yang, Jinyi Sun. Gevrey regularity and existence of Navier-Stokes-Nernst-Planck-Poisson system in critical Besov spaces. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1617-1639. doi: 10.3934/cpaa.2017078

[14]

Christina A. Hollon, Jeffrey T. Neugebauer. Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition. Conference Publications, 2015, 2015 (special) : 615-620. doi: 10.3934/proc.2015.0615

[15]

Seiji Ukai, Tong Yang, Huijiang Zhao. Exterior Problem of Boltzmann Equation with Temperature Difference. Communications on Pure & Applied Analysis, 2009, 8 (1) : 473-491. doi: 10.3934/cpaa.2009.8.473

[16]

Pierre-Étienne Druet. Higher $L^p$ regularity for vector fields that satisfy divergence and rotation constraints in dual Sobolev spaces, and application to some low-frequency Maxwell equations. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 475-496. doi: 10.3934/dcdss.2015.8.475

[17]

Khadijah Sharaf. A perturbation result for a critical elliptic equation with zero Dirichlet boundary condition. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1691-1706. doi: 10.3934/dcds.2017070

[18]

Hongmei Cao, Hao-Guang Li, Chao-Jiang Xu, Jiang Xu. Well-posedness of Cauchy problem for Landau equation in critical Besov space. Kinetic & Related Models, 2019, 12 (4) : 829-884. doi: 10.3934/krm.2019032

[19]

Marek Fila, Kazuhiro Ishige, Tatsuki Kawakami. Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1285-1301. doi: 10.3934/cpaa.2012.11.1285

[20]

Hakima Bessaih, Yalchin Efendiev, Florin Maris. Homogenization of the evolution Stokes equation in a perforated domain with a stochastic Fourier boundary condition. Networks & Heterogeneous Media, 2015, 10 (2) : 343-367. doi: 10.3934/nhm.2015.10.343

2018 Impact Factor: 0.925

Metrics

  • PDF downloads (11)
  • HTML views (0)
  • Cited by (20)

Other articles
by authors

[Back to Top]