Details
| Original language | English |
|---|---|
| Pages (from-to) | 235-269 |
| Number of pages | 35 |
| Journal | Mathematische Zeitschrift |
| Volume | 244 |
| Issue number | 2 |
| Publication status | Published - Jun 2003 |
| Externally published | Yes |
Abstract
We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted Lp-spaces over B, 1 < p < ∞. Under suitable ellipticity assumptions we can define a family of complex powers Az, z ∈ ℂ. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Mathematische Zeitschrift, Vol. 244, No. 2, 06.2003, p. 235-269.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Bounded imaginary powers of differential operators on manifolds with conical singularities
AU - Coriasco, S.
AU - Schrohe, E.
AU - Seiler, J.
N1 - Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2003/6
Y1 - 2003/6
N2 - We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted Lp-spaces over B, 1 < p < ∞. Under suitable ellipticity assumptions we can define a family of complex powers Az, z ∈ ℂ. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations.
AB - We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted Lp-spaces over B, 1 < p < ∞. Under suitable ellipticity assumptions we can define a family of complex powers Az, z ∈ ℂ. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations.
UR - http://www.scopus.com/inward/record.url?scp=0037633509&partnerID=8YFLogxK
U2 - 10.1007/s00209-003-0495-1
DO - 10.1007/s00209-003-0495-1
M3 - Article
AN - SCOPUS:0037633509
VL - 244
SP - 235
EP - 269
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 2
ER -