TY  - JOUR
A1  - Bandara, Menaka Lashitha
A1  - Rosen, Andreas
T1  - Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions
T2  - Communications in partial differential equations
N2  - On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah-Singer Dirac operator in depends Riesz continuously on perturbations of local boundary conditions The Lipschitz bound for the map depends on Lipschitz smoothness and ellipticity of and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius away from a compact neighbourhood of the boundary. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions.
KW  - Boundary value problems
KW  - Dirac operator
KW  - functional calculus
KW  - real-variable harmonic analysis
KW  - Riesz continuity
KW  - spectral flow
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/48740
SN  - 0360-5302
SN  - 1532-4133
VL  - 44
IS  - 12
SP  - 1253
EP  - 1284
PB  - Taylor & Francis Group
CY  - Philadelphia
ER  -