We study removable sets for the Sobolev space$W$^{1,p}. We show that removability for sets lying in a hyperplane is essentially determined by their thickness measured in terms of a concept of$p$-porosity.
Tiancheng Ouyang. On the positive solutions of semilinear equations Δ+-ℎ^{}=0 on the compact manifolds. 1992.
2
Arendt W, Warma M. The Laplacian with Robin Boundary Conditions on Arbitrary Domains[J]. Potential Analysis, 2003.
3
Malliavin P. Implicit Functions in Finite Corank on the Wiener Space[J]. North-holland Mathematical Library, 1984: 369-386.
4
Kilpelainen T, Koskela P. Global integrability of the gradients of solutions to partial differential equations[J]. Nonlinear Analysis-theory Methods \u0026 Applications, 1994, 23(7): 899-909.
5
Ya V M, Mitrea M, Shaposhnikova T, et al. The dirichlet problem in lipschitz domains for higher order elliptic systems with rough coefficients[J]. Journal D Analyse Mathematique, 2010, 110(1): 167-239.
6
Dynkin E M, Osilenker B P. Weighted estimates of singular integrals and their applications[J]. Journal of Mathematical Sciences, 1985, 30(3): 2094-2154.
7
Belhachmi Z, Bucur D, Burgeth B, et al. How to Choose Interpolation Data in Images[J]. Siam Journal on Applied Mathematics, 2009, 70(1): 333-352.
8
Plotnikov P I, Sokolowski J. Domain Dependence of Solutions to Compressible Navier-Stokes Equations[J]. Siam Journal on Control and Optimization, 2006, 45(4): 1165-1197.
9
Tanguy Briancon · Mohammed Hayouni · Michel Pierre. Lipschitz continuity of state functions in some optimal shaping. 2005.
10
Landes R, Mustonen V. A strongly nonlinear parabolic initial boundary value problem[J]. Arkiv för Matematik, 1987, 25(1): 29-40.
Hans Reiter. Über den Satz von Weil-Cartier. 1978.
2
Koichi Takase. On Siegel modular forms of half-integral weights and Jacobi forms. 1999.
3
Akbarov S S. Smooth structure and differential operators on a locally compact group[J]. Izvestiya: Mathematics, 1995, 59(1): 1-44.
4
Levin M D. The automorphism group of a locally compact abelian group[J]. Acta Mathematica, 1971, 127(1): 259-278.
5
Hennings M A. The Weyl transformation and quantisation for locally compact Abelian groups[J]. Publications of The Research Institute for Mathematical Sciences, 1985, 21(6): 1223-1235.
6
Igusa J. On certain representations of semi-simple algebraic groups[C]., 1971: 76-86.
7
Rubin K, Silverberg A. Ranks of elliptic curves[J]. Bulletin of the American Mathematical Society, 2002, 39(4): 455-474.