Details
| Original language | English |
|---|---|
| Pages (from-to) | 611-637 |
| Number of pages | 27 |
| Journal | Journal of differential equations |
| Volume | 257 |
| Issue number | 3 |
| Publication status | Published - 1 Aug 2014 |
Abstract
Extending earlier results on the existence of bounded imaginary powers for cone differential operators on weighted Lp-spaces Hp0,γ(B) over a manifold with conical singularities, we show how the same assumptions also yield the existence of bounded imaginary powers on higher order Mellin-Sobolev spaces Hps,γ(B), s≥0.As an application we consider the Cahn-Hilliard equation on a manifold with (possibly warped) conical singularities. Relying on our work for the case of straight cones, we first establish R-sectoriality (and thus maximal regularity) for the linearized equation and then deduce the existence of a short time solution with the help of a theorem by Clément and Li. We also obtain the short time asymptotics of the solution near the conical point.
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Journal of differential equations, Vol. 257, No. 3, 01.08.2014, p. 611-637.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Bounded imaginary powers of cone differential operators on higher order Mellin-Sobolev spaces and applications to the Cahn-Hilliard equation
AU - Roidos, Nikolaos
AU - Schrohe, Elmar
N1 - Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2014/8/1
Y1 - 2014/8/1
N2 - Extending earlier results on the existence of bounded imaginary powers for cone differential operators on weighted Lp-spaces Hp0,γ(B) over a manifold with conical singularities, we show how the same assumptions also yield the existence of bounded imaginary powers on higher order Mellin-Sobolev spaces Hps,γ(B), s≥0.As an application we consider the Cahn-Hilliard equation on a manifold with (possibly warped) conical singularities. Relying on our work for the case of straight cones, we first establish R-sectoriality (and thus maximal regularity) for the linearized equation and then deduce the existence of a short time solution with the help of a theorem by Clément and Li. We also obtain the short time asymptotics of the solution near the conical point.
AB - Extending earlier results on the existence of bounded imaginary powers for cone differential operators on weighted Lp-spaces Hp0,γ(B) over a manifold with conical singularities, we show how the same assumptions also yield the existence of bounded imaginary powers on higher order Mellin-Sobolev spaces Hps,γ(B), s≥0.As an application we consider the Cahn-Hilliard equation on a manifold with (possibly warped) conical singularities. Relying on our work for the case of straight cones, we first establish R-sectoriality (and thus maximal regularity) for the linearized equation and then deduce the existence of a short time solution with the help of a theorem by Clément and Li. We also obtain the short time asymptotics of the solution near the conical point.
UR - http://www.scopus.com/inward/record.url?scp=84901004096&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2014.04.004
DO - 10.1016/j.jde.2014.04.004
M3 - Article
AN - SCOPUS:84901004096
VL - 257
SP - 611
EP - 637
JO - Journal of differential equations
JF - Journal of differential equations
SN - 0022-0396
IS - 3
ER -