6,429 research outputs found
contraction for bounded (non-integrable) solutions of degenerate parabolic equations
We obtain new contraction results for bounded entropy solutions of
Cauchy problems for degenerate parabolic equations. The equations we consider
have possibly strongly degenerate local or non-local diffusion terms. As
opposed to previous results, our results apply without any integrability
assumption on the %(the positive part of the difference of) solutions. They
take the form of partial Duhamel formulas and can be seen as quantitative
extensions of finite speed of propagation local contraction results for
scalar conservation laws. A key ingredient in the proofs is a new and
non-trivial construction of a subsolution of a fully non-linear (dual)
equation. Consequences of our results are maximum and comparison principles,
new a priori estimates, and in the non-local case, new existence and uniqueness
results
Semi-Lagrangian schemes for linear and fully non-linear Hamilton-Jacobi-Bellman equations
We consider the numerical solution of Hamilton-Jacobi-Bellman equations
arising in stochastic control theory. We introduce a class of monotone
approximation schemes relying on monotone interpolation. These schemes converge
under very weak assumptions, including the case of arbitrary degenerate
diffusions. Besides providing a unifying framework that includes several known
first order accurate schemes, stability and convergence results are given,
along with two different robust error estimates. Finally, the method is applied
to a super-replication problem from finance.Comment: to appear in the proceedings of HYP201
Toward a Vision of Sexual and Economic Justice
This report is based on the Virginia C. Gildersleeve Lecture and colloquium at Barnard College, with keynote speakers Josephine Ho and Naomi Klein. The participants in the colloquium have all made significant contributions to our understandings of global justice as activists, artists, and scholars who have explored the meanings of economic justice and sexual justice and have worked to build links between these spheres. The aim of the workshop was to articulate connections between struggles for sexual justice and economic justice and to develop new visions of how different people and movements might come together in their efforts to create justice. This report provides a synthesis of the short thought papers the participants developed in preparation for the colloquium and their conversations during the worksho
Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations
We obtain non-symmetric upper and lower bounds on the rate of convergence of
general monotone approximation/numerical schemes for parabolic Hamilton Jacobi
Bellman Equations by introducing a new notion of consistency. We apply our
general results to various schemes including finite difference schemes,
splitting methods and the classical approximation by piecewise constant
controls
Continuous dependence results for Non-linear Neumann type boundary value problems
We obtain estimates on the continuous dependence on the coefficient for
second order non-linear degenerate Neumann type boundary value problems. Our
results extend previous work of Cockburn et.al., Jakobsen-Karlsen, and
Gripenberg to problems with more general boundary conditions and domains. A new
feature here is that we account for the dependence on the boundary conditions.
As one application of our continuous dependence results, we derive for the
first time the rate of convergence for the vanishing viscosity method for such
problems. We also derive new explicit continuous dependence on the coefficients
results for problems involving Bellman-Isaacs equations and certain quasilinear
equation
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