Bounded imaginary powers of differential operators on manifolds with conical singularities

By Sandro Coriasco, Elmar Schrohe, J. Seiler. 2001

51 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/45dae87ccb7315914e427b5bf2aac8a4f79399db

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In Applied Mathematics

1. Elmar Schrohe
2. J. Seiler
3. Victor Nistor
4. Bernd Ammann
5. András Vasy
6. Gerd Grubb
7. N. Roidos

In Control and Systems Engineering

1. Elmar Schrohe
2. J. Seiler
3. András Vasy

Citations in the corpus

• Adjoints of elliptic cone operators (2001, unknown): “See also Coriasco, Schrohe, and Seiler [13].”
• Complex Powers and Non-compact Manifolds (2002, background): “ferential operators have proved useful to study the asymptotic of eigenvalues of self-adjoint pseudodifferential operators [11], Sobolev spaces, and even certain nonlinear differential equations (see [ 8 , 35, 9] and the references therein).”
• The Resolvent of Closed Extensions of Cone Differential Operators (2002, methodology): “5 in [3] that the structure of the resolvent we obtain from Theorem 3.”