265 research outputs found
Carleman estimates and absence of embedded eigenvalues
Let L be a Schroedinger operator with potential W in L^{(n+1)/2}. We prove
that there is no embedded eigenvalue. The main tool is an Lp Carleman type
estimate, which builds on delicate dispersive estimates established in a
previous paper. The arguments extend to variable coefficient operators with
long range potentials and with gradient potentials.Comment: 26 page
Decay estimates for variable coefficient wave equations in exterior domains
In this article we consider variable coefficient, time dependent wave
equations in exterior domains. We prove localized energy estimates if the
domain is star-shaped and global in time Strichartz estimates if the domain is
strictly convex.Comment: 15 pages. In the new version, some typos are fixed and a minor
correction was made to the proof of Lemma 1
Koszul-Tate Cohomology For an Sp(2)-Covariant Quantization of Gauge Theories with Linearly Dependent Generators
The anti-BRST transformation, in its Sp(2)-symmetric version, for the general
case of any stage-reducible gauge theories is implemented in the usual BV
approach. This task is accomplished not by duplicating the gauge symmetries but
rather by duplicating all fields and antifields of the theory and by imposing
the acyclicity of the Koszul-Tate differential. In this way the Sp(2)-covariant
quantization can be realised in the standard BV approach and its equivalence
with BLT quantization can be proven by a special gauge fixing procedure.Comment: 13 pages, Latex, To Be Published in International Journal of Modern
Physics
Irreducible Hamiltonian BRST-anti-BRST symmetry for reducible systems
An irreducible Hamiltonian BRST-anti-BRST treatment of reducible first-class
systems based on homological arguments is proposed. The general formalism is
exemplified on the Freedman-Townsend model.Comment: LaTeX 2.09, 35 page
Sharp Hadamard local well-posedness, enhanced uniqueness and pointwise continuation criterion for the incompressible free boundary Euler equations
We provide a complete local well-posedness theory in based Sobolev
spaces for the free boundary incompressible Euler equations with zero surface
tension on a connected fluid domain. Our well-posedness theory includes: (i)
Local well-posedness in the Hadamard sense, i.e., local existence, uniqueness,
and the first proof of continuous dependence on the data, all in low regularity
Sobolev spaces; (ii) Enhanced uniqueness: Our uniqueness result holds at the
level of the Lipschitz norm of the velocity and the
regularity of the free surface; (iii) Stability bounds: We construct a
nonlinear functional which measures, in a suitable sense, the distance between
two solutions (even when defined on different domains) and we show that this
distance is propagated by the flow; (iv) Energy estimates: We prove refined,
essentially scale invariant energy estimates for solutions, relying on a newly
constructed family of elliptic estimates; (v) Continuation criterion: We give
the first proof of a sharp continuation criterion in the physically relevant
pointwise norms, at the level of scaling. In essence, we show that solutions
can be continued as long as the velocity is in and the free
surface is in , which is at the same level as the
Beale-Kato-Majda criterion for the boundaryless case; (vi) A novel proof of the
construction of regular solutions.
Our entire approach is in the Eulerian framework and can be adapted to work
in more general fluid domains.Comment: 117 pages, some typos correcte
Energy dispersed large data wave maps in 2+1 dimensions
In this article we consider large data Wave-Maps from into
a compact Riemannian manifold , and we prove that regularity
and dispersive bounds persist as long as a certain type of bulk
(non-dispersive) concentration is absent. In a companion article we use these
results in order to establish a full regularity theory for large data
Wave-Maps.Comment: 89 page
A new approach to hyperbolic inverse problems
We present a modification of the BC-method in the inverse hyperbolic
problems. The main novelty is the study of the restrictions of the solutions to
the characteristic surfaces instead of the fixed time hyperplanes. The main
result is that the time-dependent Dirichlet-to-Neumann operator prescribed on a
part of the boundary uniquely determines the coefficients of the self-adjoint
hyperbolic operator up to a diffeomorphism and a gauge transformation. In this
paper we prove the crucial local step. The global step of the proof will be
presented in the forthcoming paper.Comment: We corrected the proof of the main Lemma 2.1 by assuming that
potentials A(x),V(x) are real value
Covariant Effective Action for Quantum Particle with Coordinate-Dependent Mass
Using a covariant background field method we calculate the one-loop quantum
effective action for a particle with coordinate-dependent mass moving slowly
through a one-dimensional configuration space. The procedure can easily be
extended to any desired loop order.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper (including all PS fonts) at
http://www.physik.fu-berlin.de/~kleinert/31
Global well-posedness of the KP-I initial-value problem in the energy space
We prove that the KP-I initial value problem is globally well-posed in the
natural energy space of the equation
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