20,757 research outputs found
Recent works on the Strauss conjecture
In this review paper, we summarize the current state-of-art on the Strauss
conjecture with nontrapping obstacles. Among others, three essential estimates
are emphasized and presented: Morawetz-KSS estimates (also known as local
energy estimates), weighted Strichartz estimates and generalized Strichartz
estimates.Comment: 21 pages, no figures. No changes in content, but disable the usage of
the package showkey
Perturbations of Functional Inequalities for L\'evy Type Dirichlet Forms
Perturbations of super Poincar\'e and weak Poincar\'e inequalities for L\'evy
type Dirichlet forms are studied. When the range of jumps is finite our results
are natural extensions to the corresponding ones derived earlier for diffusion
processes; and we show that the study for the situation with infinite range of
jumps is essentially different. Some examples are presented to illustrate the
optimality of our results
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