Multipliers as Solutions to Elliptic Equations

In Sects. 13.1–13.3 of this chapter, solutions of second-order linear and quasilinear elliptic differential equations and systems are considered as multipliers in certain spaces of differentiable functions in a domain Ω. On one hand, this can be of interest for the theory of functions, since it leads to new characterizations of multipliers and, on the other hand, for the theory of partial differential equations, since it allows us to obtain a priori information about the solutions in spaces different from the usual ones.

In Sect. 13.4 we obtain coercive estimates in multiplier spaces for solutions of linear elliptic systems in a half-space. The last Sect. 13.5 is devoted to regularity of solutions to higher order semilinear elliptic equations.