Sharp regularity theory for thermo-elastic mixed problems¹

¹Research partially supported by the National Science Foundation under Grant DMS-904822, and by the Army Research Office under Grant DAAH04-96-1-0059

Abstract

We give a sharp (optimal) regularity theory of thermo-elastic mixed problems. Our approach is by P.D.E. methods and applies to any space dimension and, in principle, to any set of boundary conditions. We consider two sets of boundary conditions: hinged and clamped B.C. The original coupled P.D.E. system is split into two suitable uncoupled P.D.E. equations: a Kirchoff mixed problem and a heat equation, whose delicate, optimal regularity is available in the literature. Ultimately, the original problem with boundary non-homogeneous term is reduced to the same problem, however, with homogeneou B.C. and a known ‘right-hand term’ in the equation, which is easier to analyze.

Keywords:

• kirchoff equation
• semigroup

AMS:

• 35Q99
• 73C99

¹Research partially supported by the National Science Foundation under Grant DMS-904822, and by the Army Research Office under Grant DAAH04-96-1-0059

¹Research partially supported by the National Science Foundation under Grant DMS-904822, and by the Army Research Office under Grant DAAH04-96-1-0059

Notes

¹Research partially supported by the National Science Foundation under Grant DMS-904822, and by the Army Research Office under Grant DAAH04-96-1-0059