A Note on the Displacement Problem of Elastostatics with Singular Boundary Values

Abstract

The displacement problem of linear elastostatics in bounded and exterior domains with a non-regular boundary datum a is considered. Precisely, if the elastic body is represented by a domain of class C k ( k ≥ 2 ) of R 3 and a ∈ W 2 − k − 1 / q , q ( ∂ Ω ) , q ∈ ( 1 , + ∞ ) , then it is proved that there exists a solution which is of class C ∞ in the interior and takes the boundary value in a well-defined sense. Moreover, it is unique in a natural function class.

Mathematical Analysis and Applications II

“…Web Site: http://www.math.uvic.ca/faculty/harimsri/ The present volume contains the invited, accepted and published submissions (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]) to a Special Issue of the MDPI's journal, Axioms, on the subject-area of "Mathematical Analysis and Applications II". A successful predecessor of this volume happens to be the Special Issue of the MDPI's journal, Axioms, on the subject-area of "Mathematical Analysis and Applications" (see, for details, [18]).…”