R. Duduchava

A Revised Asymptotic Model of a Shell

abstract:
Asymptotic model of a shell (Koiter, Sanchez-Palencia, Ciarlet etc.) is revised based on the calculus of tangent Gunter's derivatives, developed in the recent papers of the author with D. Mitrea and M. Mitrea. [R Duduchava, Pseudodifferential operators with applications to some problems of mathematical physics. (Lectures at Stuttgart University, Fall semester 2001-2002).Universität Stuttgart, 2002, Preprint 2002-6, 1-176], [R. Duduchava, Lions's lemma, Korn's inequalities and Lam'e operator on hypersurfaces. Oper. Theory Adv. Appl. 210 (2010), 43-77, Springer Basel AG], [R. Duduchava, Partial differential equations on hypersurfaces. Mem. Differential Equations Math. Phys. 48 (2009), 19-74], [R. Duduchava, D. Mitrea, and M. Mitrea, Differential operators and boundary value problems on hypersurfaces. Math. Nachr. 279 (2006), No. 9-10, 996-1023]. As a result the 2-dimensional shell equation on a middle surface $\mathcal{S}$ is written in terms of Gunter's derivatives, unit normal vector field and the Lam\'e constant, which coincides with the Lam\'e equation on the hypersurface $\mathcal{S}$, investigated in the papers mentioned above.

Mathematics Subject Classification: Primary 35J57; Secondary 74J35, 58J32

Key words and phrases: Shell, Gunter's derivative, Korn's inequality, Killing's vector fields, Lax-Milgram lemma, Lam\'e equation, boundary value problems