Sharp regularity theory for thermo-elastlc mixed problems

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. In one approach, 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 either available in, or can be deduced by duality from, the literature. Ultimately, the original problem with boundary non-homogeneous term is reduced to the same problem, however, with homogeneous B.C. and a known 'right-hand term' in the equation, which is easier to analyze. A direct proof is also given in the seriously more demanding clamped case.

Keywords:

• Regularity theory
• Kirchoff equations
• semigroups

AMS:

• 35Q99
• 73C99