We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Fredholm and regularity theory of Douglis-Nirenberg elliptic systems on $${\mathbb{R}^{N}}$$.
- Authors
Rabier, Patrick
- Abstract
We give a fairly complete exposition of the Fredholm properties of the Douglis-Nirenberg elliptic systems on $${\mathbb{R}^{N}}$$ in the classical (unweighted) L Sobolev spaces and under 'minimal' assumptions about the coefficients. These assumptions rule out the use of classical pseudodifferential operator theory, although it is indirectly of assistance in places. After generalizing a necessary and sufficient condition for Fredholmness, already known in special cases, various invariance properties are established (index, null space, etc.), with respect to p and the Douglis-Nirenberg numbers. Among other things, this requires getting around the problem that the L spaces are not ordered by inclusion. In turn, with some work, invariance leads to a regularity theory more general than what can be obtained by the method of differential quotients.
- Subjects
FREDHOLM equations; INTEGRAL equations; SOBOLEV spaces; SOBOLEV gradients; OPERATOR theory
- Publication
Mathematische Zeitschrift, 2012, Vol 270, Issue 1/2, p369
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-010-0802-6