American Institute of Mathematical Sciences

October  2005, 13(5): 1097-1124. doi: 10.3934/dcds.2005.13.1097

Topology of Sobolev mappings IV

 1 Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States 2 Department of Mathematics, New York University, 251 Mercer St. New York, NY 10012, United States

Received  September 2004 Revised  February 2005 Published  September 2005

We will classify the path connected components of spaces of Sobolev maps between manifolds and study the strong and weak density of smooth maps in the spaces of Sobolev maps for the case the domain manifold has nonempty boundary and Dirichlet problems.
Citation: Fengbo Hang, Fanghua Lin. Topology of Sobolev mappings IV. Discrete & Continuous Dynamical Systems - A, 2005, 13 (5) : 1097-1124. doi: 10.3934/dcds.2005.13.1097
 [1] Navin Keswani. Homotopy invariance of relative eta-invariants and $C^*$-algebra $K$-theory. Electronic Research Announcements, 1998, 4: 18-26. [2] Ruyun Ma, Man Xu. Connected components of positive solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2701-2718. doi: 10.3934/dcdsb.2018271 [3] Giuseppe Buttazzo, Eugene Stepanov. Transport density in Monge-Kantorovich problems with Dirichlet conditions. Discrete & Continuous Dynamical Systems - A, 2005, 12 (4) : 607-628. doi: 10.3934/dcds.2005.12.607 [4] Grzegorz Graff, Jerzy Jezierski. Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds. Conference Publications, 2011, 2011 (Special) : 523-532. doi: 10.3934/proc.2011.2011.523 [5] Anna Karnauhova, Stefan Liebscher. Connected components of meanders: Ⅰ. bi-rainbow meanders. Discrete & Continuous Dynamical Systems - A, 2017, 37 (9) : 4835-4856. doi: 10.3934/dcds.2017208 [6] Hiroki Sumi. Dynamics of postcritically bounded polynomial semigroups I: Connected components of the Julia sets. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 1205-1244. doi: 10.3934/dcds.2011.29.1205 [7] Geng Chen, Ronghua Pan, Shengguo Zhu. A polygonal scheme and the lower bound on density for the isentropic gas dynamics. Discrete & Continuous Dynamical Systems - A, 2019, 39 (7) : 4259-4277. doi: 10.3934/dcds.2019172 [8] Anatole Katok, Federico Rodriguez Hertz. Uniqueness of large invariant measures for $\mathbb{Z}^k$ actions with Cartan homotopy data. Journal of Modern Dynamics, 2007, 1 (2) : 287-300. doi: 10.3934/jmd.2007.1.287 [9] Robert Carlson. Dirichlet to Neumann maps for infinite quantum graphs. Networks & Heterogeneous Media, 2012, 7 (3) : 483-501. doi: 10.3934/nhm.2012.7.483 [10] Yuhua Sun, Zilong Wang, Hui Li, Tongjiang Yan. The cross-correlation distribution of a $p$-ary $m$-sequence of period $p^{2k}-1$ and its decimated sequence by $\frac{(p^{k}+1)^{2}}{2(p^{e}+1)}$. Advances in Mathematics of Communications, 2013, 7 (4) : 409-424. doi: 10.3934/amc.2013.7.409 [11] Tiancong Chen, Qing Han. Smooth local solutions to Weingarten equations and $\sigma_k$-equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 653-660. doi: 10.3934/dcds.2016.36.653 [12] Viviane Baladi, Daniel Smania. Smooth deformations of piecewise expanding unimodal maps. Discrete & Continuous Dynamical Systems - A, 2009, 23 (3) : 685-703. doi: 10.3934/dcds.2009.23.685 [13] Yong Fang. On smooth conjugacy of expanding maps in higher dimensions. Discrete & Continuous Dynamical Systems - A, 2011, 30 (3) : 687-697. doi: 10.3934/dcds.2011.30.687 [14] Ralf Spatzier, Lei Yang. Exponential mixing and smooth classification of commuting expanding maps. Journal of Modern Dynamics, 2017, 11: 263-312. doi: 10.3934/jmd.2017012 [15] Baoquan Yuan, Xiaokui Zhao. Blowup of smooth solutions to the full compressible MHD system with compact density. Kinetic & Related Models, 2014, 7 (1) : 195-203. doi: 10.3934/krm.2014.7.195 [16] Jing Quan, Zhiyou Wu, Guoquan Li. Global optimality conditions for some classes of polynomial integer programming problems. Journal of Industrial & Management Optimization, 2011, 7 (1) : 67-78. doi: 10.3934/jimo.2011.7.67 [17] L. Búa, T. Mestdag, M. Salgado. Symmetry reduction, integrability and reconstruction in $k$-symplectic field theory. Journal of Geometric Mechanics, 2015, 7 (4) : 395-429. doi: 10.3934/jgm.2015.7.395 [18] Guolin Yu. Global proper efficiency and vector optimization with cone-arcwise connected set-valued maps. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 35-44. doi: 10.3934/naco.2016.6.35 [19] Cristina Lizana, Vilton Pinheiro, Paulo Varandas. Contribution to the ergodic theory of robustly transitive maps. Discrete & Continuous Dynamical Systems - A, 2015, 35 (1) : 353-365. doi: 10.3934/dcds.2015.35.353 [20] Silvia Frassu. Nonlinear Dirichlet problem for the nonlocal anisotropic operator $L_K$. Communications on Pure & Applied Analysis, 2019, 18 (4) : 1847-1867. doi: 10.3934/cpaa.2019086

2018 Impact Factor: 1.143