American Institute of Mathematical Sciences

Advanced
January  2007, 18(1): 121-134. doi: 10.3934/dcds.2007.18.121

Lp regularity theory for linear elliptic systems

Sun-Sig Byun 1, , Hongbin Chen 2, , Mijoung Kim 1, and  Lihe Wang 3,

1. 

Department of Mathematical Sciences, Seoul National University, Seoul 151-747, South Korea, South Korea
2. 

College of Sciences, Xian Jiaotong University, Xian 710049, China
3. 

Department of Mathematics, University of Iowa, Iowa City, IA 52242, United States

Received  April 2006 Revised  November 2006 Published  February 2007

We consider the conormal derivative problem for an elliptic system in divergence form with discontinuous coefficients in a more general geometric setting. We obtain the $L^{p}$, $1 < p <\infty$, regularity of the maximum order derivatives of the weak solutions for such a problem.
Keywords: $L^{p}$ estimates, elliptic system, BMO space, Reifenberg Domain..
Mathematics Subject Classification: Primary: 35R05, 35R35; Secondary: 35J15, 35J2.
Citation: Sun-Sig Byun, Hongbin Chen, Mijoung Kim, Lihe Wang. Lp regularity theory for linear elliptic systems. Discrete & Continuous Dynamical Systems - A, 2007, 18 (1) : 121-134. doi: 10.3934/dcds.2007.18.121
[1]

Sun-Sig Byun, Lihe Wang. $W^{1,p}$ regularity for the conormal derivative problem with parabolic BMO nonlinearity in reifenberg domains. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 617-637. doi: 10.3934/dcds.2008.20.617
[2]

N. V. Krylov. Some $L_{p}$-estimates for elliptic and parabolic operators with measurable coefficients. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 2073-2090. doi: 10.3934/dcdsb.2012.17.2073
[3]

Junjie Zhang, Shenzhou Zheng. Weighted lorentz estimates for nondivergence linear elliptic equations with partially BMO coefficients. Communications on Pure & Applied Analysis, 2017, 16 (3) : 899-914. doi: 10.3934/cpaa.2017043
[4]

Kyeong-Hun Kim, Kijung Lee. A weighted $L_p$-theory for second-order parabolic and elliptic partial differential systems on a half space. Communications on Pure & Applied Analysis, 2016, 15 (3) : 761-794. doi: 10.3934/cpaa.2016.15.761
[5]

Jinrui Huang, Wenjun Wang, Huanyao Wen. On $ L^p $ estimates for a simplified Ericksen-Leslie system. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1485-1507. doi: 10.3934/cpaa.2020075
[6]

Mei Ming. Weighted elliptic estimates for a mixed boundary system related to the Dirichlet-Neumann operator on a corner domain. Discrete & Continuous Dynamical Systems - A, 2019, 39 (10) : 6039-6067. doi: 10.3934/dcds.2019264
[7]

Samer Dweik. $ L^{p, q} $ estimates on the transport density. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3001-3009. doi: 10.3934/cpaa.2019134
[8]

Dung Le. On the regular set of BMO weak solutions to $p$-Laplacian strongly coupled nonregular elliptic systems. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3245-3265. doi: 10.3934/dcdsb.2014.19.3245
[9]

Fabrice Planchon, John G. Stalker, A. Shadi Tahvildar-Zadeh. $L^p$ Estimates for the wave equation with the inverse-square potential. Discrete & Continuous Dynamical Systems - A, 2003, 9 (2) : 427-442. doi: 10.3934/dcds.2003.9.427
[10]

Seung-Yeal Ha, Mitsuru Yamazaki. $L^p$-stability estimates for the spatially inhomogeneous discrete velocity Boltzmann model. Discrete & Continuous Dynamical Systems - B, 2009, 11 (2) : 353-364. doi: 10.3934/dcdsb.2009.11.353
[11]

Antonio Vitolo. $H^{1,p}$-eigenvalues and $L^\infty$-estimates in quasicylindrical domains. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1315-1329. doi: 10.3934/cpaa.2011.10.1315
[12]

Andrea Cianchi, Vladimir Maz'ya. Global gradient estimates in elliptic problems under minimal data and domain regularity. Communications on Pure & Applied Analysis, 2015, 14 (1) : 285-311. doi: 10.3934/cpaa.2015.14.285
[13]

Umberto De Maio, Peter I. Kogut, Gabriella Zecca. On optimal $ L^1 $-control in coefficients for quasi-linear Dirichlet boundary value problems with $ BMO $-anisotropic $ p $-Laplacian. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020021
[14]

Karen Yagdjian, Anahit Galstian. Fundamental solutions for wave equation in Robertson-Walker model of universe and $L^p-L^q$ -decay estimates. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 483-502. doi: 10.3934/dcdss.2009.2.483
[15]

Masahiro Ikeda, Takahisa Inui, Mamoru Okamoto, Yuta Wakasugi. $ L^p $-$ L^q $ estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data. Communications on Pure & Applied Analysis, 2019, 18 (4) : 1967-2008. doi: 10.3934/cpaa.2019090
[16]

Tadeusz Iwaniec, Gaven Martin, Carlo Sbordone. $L^p$-integrability & weak type $L^{2}$-estimates for the gradient of harmonic mappings of $\mathbb D$. Discrete & Continuous Dynamical Systems - B, 2009, 11 (1) : 145-152. doi: 10.3934/dcdsb.2009.11.145
[17]

Ogabi Chokri. On the $L^p-$ theory of Anisotropic singular perturbations of elliptic problems. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1157-1178. doi: 10.3934/cpaa.2016.15.1157
[18]

Chérif Amrouche, Huy Hoang Nguyen. Elliptic problems with $L^1$-data in the half-space. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 369-397. doi: 10.3934/dcdss.2012.5.369
[19]

Shuying He, Rumei Zhang, Fukun Zhao. A note on a superlinear and periodic elliptic system in the whole space. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1149-1163. doi: 10.3934/cpaa.2011.10.1149
[20]

Mathias Wilke. $L_p$-theory for a Cahn-Hilliard-Gurtin system. Evolution Equations & Control Theory, 2012, 1 (2) : 393-429. doi: 10.3934/eect.2012.1.393

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (183)
  • HTML views (0)
  • Cited by (22)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences