Exponential Decay and Regularity for SG-elliptic Operators with Polynomial Coefficients
Marco Cappiello, Todor V. Gramchev, Luigi Rodino · Birkhäuser Basel eBooks · 2007
We study the exponential decay and the regularity for solutions of elliptic partial differential equations Pu=f , globally defined in ℝ n . In particular, we consider linear operators with polynomial coefficients which are SG-elliptic at infinity. Starting from f in the so-called Gelfand-Shilov spaces, the solutions u∈S of the equation are proved to belong to the same classes. Proofs are based on a priori estimates and arguments on the Newton polyhedron associated to the operator P .