The existence, uniqueness, and continuous dependence on the data are investigated for the weak solutions of boundary integral equations arising in the interior and exterior Dirichlet and Neumann problems for plates with transverse shear deformation treated by means of potential methods.
[1] Constanda, C.: A mathematical analysis of bending of plates with transverse shear deformation, Pitman Res. Notes Math. Ser. 215, Longman, Harlow, 1990.
2.
[2] Constanda, C.: On integral solutions of the equations of thin plates. Proc. Roy. Soc. London Ser A., 444, 317-323 (1994).
3.
[3] Constanda, C.: Fredholm equations of the first kind in the theory of bending of elastic plates. Quart. J. Mech. Appl. Math., 50, 85-96 (1997).
4.
[4] Constanda, C.: On the direct and indirect methods in the theory of elastic plates. Math. Mech. Solids, 1, 251-260 (1996).
5.
[5] Constanda, C.: Elastic boundary conditions in the theory of plates. Math. Mech. Solids, 2, 189-197 (1997).
6.
[6] Schiavone, P: On the Robin problem for the equations of thin plates. J. Integral Equations Appl., 8, 231-238 (1996).
7.
[7] Schiavone, P: Mixed problems in the theory of bending of elastic plates with transverse shear deformation. Quart. J. Mech. Appl. Math., 50, 239-249 (1997).
8.
[8] Chudinovich, I.Yu.: The Boundary Equation Method in Problems of Dynamics of Elastic Media, Kharkov University Press, Kharkov, 1991 (Russian).
9.
[9] Chudinovich, I. Yu.: Methods of potential theory in the dynamics of elastic media. Russian J. Math. Phys., 1, 427-446 (1993).
10.
[10] Chudinovich, I.Yu.: The boundary equation method in the third initial boundary value problem of the theory of elasticity. Math. Methods Appl. Sci., 16, 203-227 (1993).
11.
[11] Duvaut, G. and Lions, J.-L.: Inequalities in Mechanics and Physics, Springer-Verlag, Berlin, 1976.
12.
[12] Chudinovich, I. and Constanda, C.: Weak solutions of interior boundary value problems for plates with transverse shear deformation. IMA J. Appl. Math., 59, 85-94 (1997).
13.
[13] Chudinovich, I. and Constanda, C.: Variational treatment of exterior boundary value problems for thin elastic plates. IMA J. Appl. Math., 61, 1-14 (1998).
14.
14] Chudinovich, I. and Constanda, C.: Displacement-traction boundary value problems for elastic plates with transverse shear deformation. J. Integral Equations Appl., 11, 421-436 (1999).
