Solution in Quadratures of the Basic Problems of Thermoelasticity for a Sphere and a Spherical Cavity

The basic static problems of classical thermoelasticity are solved in quadratures for a sphere and the entire space with a spherical cavity. The solution is constructed under the most general and natural restrictions. Many boundary value problems of mathematical physics are reduced by means of special potentials to singular integral equations. For some domains these equations are solved explicitly and solutions of the corresponding boundary value problems are constructed in quadratures. For domains with a spherical boundary it appears to be convenient to use a special representation of solutions sometimes called the Trefftz representation (see, for example, [9] or [16]) but evidently occuring for the first time as early as 1904 in a paper of Marcolongo [11]. It is shown that this representation is also valid for problems of thermoelasticity.