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.
Yurii I. LyubarskiiDepartment of Mathematical Sciences, Norwegian University of Science and TechnologyAlexander RashkovskiiInstitute for Low Temperature Physics & Engineering, 47, Lenin pr., Kharkov, Ukraine
Agmon S, Nirenberg L. Properties of solutions of ordinary differential equations in banach space[J]. Communications on Pure and Applied Mathematics, 1963, 16(2): 121-239.
2
Kaplan S. On the growth of solutions of quasi‐linear parabolic equations[J]. Communications on Pure and Applied Mathematics, 1963, 16(3): 305-330.
3
Paul Fife. Solutions of parabolic boundary problems existing for all time. 1964.
4
Denisov V N. On the behaviour of solutions of parabolic equations for large values of time[J]. Russian Mathematical Surveys, 2005, 60(4): 721-790.
5
R S Anderssen. The character of non-uniqueness in the conductivity modelling problem for the earth. 1970.
6
Arosio A. Asymptotic behaviour as of solutions of linear parabolic equations with discontinuous coefficients in[J]. Communications in Partial Differential Equations, 1979, 4(7): 769-794.
7
Gekeler E. Long-Range and Periodic Solutions of Parabolic Problems[J]. Mathematische Zeitschrift, 1973, 134(1): 53-66.
8
Ilyin A M, Kalashnikov A S, Oleynik O A, et al. Linear Second-Order Partial Differential Equations of the Parabolic Type[J]. Journal of Mathematical Sciences, 2002.
9
Pazy A. Asymptotic behavior of the solution of an abstract evolution equation and some applications[J]. Journal of Differential Equations, 1968, 4(4): 493-509.
10
Ju N Ceremnyh. THE BEHAVIOR OF SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND ORDER PARABOLIC EQUATIONS AS t GROWS WITHOUT BOUND. 1968.