Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 54, pp. 1-33.

Title: Nash-Moser techniques for nonlinear boundary-value problems

Author: Markus Poppenberg (Univ. Dortmund, Germany)

Abstract: 
 A new linearization method is introduced for smooth
 short-time solvability of initial boundary value problems for
 nonlinear evolution equations. The technique based on an inverse
 function theorem of Nash-Moser type is illustrated by an
 application in the parabolic case. The equation and the boundary
 conditions may depend fully nonlinearly on time and space
 variables. The necessary compatibility conditions are transformed
 using a Borel's theorem. A general trace theorem for normal
 boundary conditions is proved in spaces of smooth functions by
 applying tame splitting theory in Frechet spaces. The
 linearized parabolic problem is treated using maximal regularity
 in analytic semigroup theory, higher order elliptic a priori
 estimates and simultaneous continuity in trace theorems in Sobolev
 spaces.
 
Submitted July 14, 2002. Published May 5, 2003.
Math Subject Classifications: 35K60, 58C15, 35K30.
Key Words: Nash-Moser; inverse function theorem;
           boundary-value problem; parabolic; analytic semigroup; 
	   evolution system; maximal regularity; trace theorem.