This paper is concerned with a class of semilinear hyperbolic equations with singular
potentials on the manifolds with conical singularities, which was introduced to describe a …

We consider abstract non-negative self-adjoint operators on L 2 (X) which satisfy the finite-
speed propagation property for the corresponding wave equation. For such operators, we …

Let (M, g) be a compact, boundaryless manifold of dimension n with the property that either
(i) n= 2 and (M, g) has no conjugate points, or (ii) the sectional curvatures of (M, g) are …

We study the L 1→ L∞-decay estimates for the Klein-Gordon equation in the Aharonov-
Bohm magnetic fields, and further prove Strichartz estimates for the Klein-Gordon equation …

Let $ M^\circ $ be a complete noncompact manifold and $ g $ an asymptotically conic
Riemaniann metric on $ M^\circ $, in the sense that $ M^\circ $ compactifies to a manifold …

We prove global-in-time Strichartz estimates without loss of derivatives for the solution of the
Schrödinger equation on a class of nontrap** asymptotically conic manifolds. We obtain …

On doubling metric measure spaces endowed with a strongly local regular Dirichlet form, we
show some characterisations of pointwise upper bounds of the heat kernel in terms of global …

Let HV be a self-adjoint extension of the Schrödinger operator− Δ+ V (x) with the Dirichlet
boundary condition on an arbitrary open set Ω of Rd, where d≥ 1 and the negative part of …

Consider the metric cone X= C (Y)=(0, ∞) _r * YX= C (Y)=(0,∞) r× Y with metric g= dr^ 2+ r^
2h g= dr 2+ r 2 h where the cross section Y is a compact (n-1)(n-1)-dimensional Riemannian …

We prove the global-in-time Strichartz estimates for wave equations on the nontrap**
asymptotically conic manifolds. We obtain estimates for the full set of wave admissible …