Resolvent Estimates for Singularly Perturbed Elliptic Operators in Hölder Spaces

✍ Scribed by Branko Najman

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 508 KB
• Volume: 184
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19971840111

✦ Synopsis

Abstract

The norm of the inverse operator of ϵ__A + B__ ‐ λ__I__ between the Besov spaces B, ∞ (Ω) and B^t^∞,∞(Ω) is estimated, where A and B are uniformly elliptic operators with smooth coefficients and Dirichlet boundary conditions, A is of order 2__m, B__ of order 2__m, m > m'__. The estimate holds for negative t. The Besov space B, ∞ (Ω) reduces to the space of Hölder continuous functions C^s^ (Ω) if s < 0 is non – integer.

In particular, it is shown that Aϵ generates an analytic semigroup in B, ∞ (Ω), s ϵ (‐1,0), if Ω = ℝ__^n^__ or ℝ and A, B are constant coefficient operators without lower order terms.