4,163 research outputs found
Multi-valued, singular stochastic evolution inclusions
We provide an abstract variational existence and uniqueness result for
multi-valued, monotone, non-coercive stochastic evolution inclusions in Hilbert
spaces with general additive and Wiener multiplicative noise. As examples we
discuss certain singular diffusion equations such as the stochastic 1-Laplacian
evolution (total variation flow) in all space dimensions and the stochastic
singular fast diffusion equation. In case of additive Wiener noise we prove the
existence of a unique weak-* mean ergodic invariant measure.Comment: 39 pages, in press: J. Math. Pures Appl. (2013
Elliptic theory of differential edge operators, II: boundary value problems
This is a continuation of the first author's development of the theory of
elliptic differential operators with edge degeneracies. That first paper
treated basic mapping theory, focusing on semi-Fredholm properties on weighted
Sobolev and H\"older spaces and regularity in the form of asymptotic expansions
of solutions. The present paper builds on this through the formulation of
boundary conditions and the construction of parametrices for the associated
boundary problems. As before, the emphasis is on the geometric microlocal
structure of the Schwartz kernels of parametrices and generalized inverses.Comment: 45 pages, 3 figure
Gluing and wormholes for the Einstein constraint equations
We establish a general gluing theorem for constant mean curvature solutions
of the vacuum Einstein constraint equations. This allows one to take connected
sums of solutions or to glue a handle (wormhole) onto any given solution. Away
from this handle region, the initial data sets we produce can be made as close
as desired to the original initial data sets. These constructions can be made
either when the initial manifold is compact or asymptotically Euclidean or
asymptotically hyperbolic, with suitable corresponding conditions on the
extrinsic curvature. In the compact setting a mild nondegeneracy condition is
required. In the final section of the paper, we list a number ways this
construction may be used to produce new types of vacuum spacetimes.Comment: 42 pages, 4 figures, minor typos corrected, 1 reference added. To
appear in Comm. Math. Phys. v3 (v2 had old Latex source file
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