Schauder estimates and existence theory for entire solutions of linear parabolic equations
Christopher Mawata · Differential and Integral Equations · 1989
Solutions in Rn+l of the linear, parabolic, nonhomogeneous partial differential equation and the related homogeneous equation are investigated.By entire solutions is meant solutions of these equations defined in all of Rn+ 1 .Schauder-type a priori estimates are developed for entire solutions with prescribed behavior at infinity.These estimates lead to an existence theory for entire solutions with certain behavior required at infinity.Uniqueness of these solutions follows from the maximum principle.