Perturbation of well-posedness and layer potentials for higher-order elliptic systems with rough coefficients

TL;DR

This paper investigates the stability of well-posed boundary value problems for higher-order elliptic systems with rough coefficients, focusing on perturbations and fractional boundary data, and establishes new well-posedness results.

Contribution

It provides $L^ abla$ perturbation results for well-posedness of higher-order elliptic boundary problems with fractional boundary data, extending previous findings.

Findings

Established $L^ abla$ perturbative well-posedness results for inhomogeneous problems.

Proved new well-posedness results for second-order operators with near-real, t-independent coefficients.

Extended results to fourth-order operators close to the biharmonic operator.

Abstract

In this paper we study boundary value problems for higher order elliptic differential operators in divergence form. We consider the two closely related topics of inhomogeneous problems and problems with boundary data in fractional smoothness spaces. We establish $L^\infty$ perturbative results concerning well posedness of inhomogeneous problems with boundary data in fractional smoothness spaces. Combined with earlier known results, this allows us to establish new well posedness results for second order operators whose coefficients are close to being real and t-independent and for fourth-order operators close to the biharmonic operator.