منابع مشابه
Regularity Results for Eikonal-Type Equations with Nonsmooth Coefficients
Solutions of the Hamilton-Jacobi equation H(x,−Du(x)) = 1, with H(·, p) Hölder continuous and H(x, ·) convex and positively homogeneous of degree 1, are shown to be locally semiconcave with a power-like modulus. An essential step of the proof is the C-regularity of the extremal trajectories associated with the multifunction generated by DpH .
متن کاملFurther results on generalized Kapteyn-type expansions
In memoriam Csörgő Sándor, dear friend and great scholar Keywords: Bessel function of first kind J ν (z) Bounds for J ν (z) Positive zeros j ν,s of J ν (z) Generalized Kapteyn expansion Kapteyn series a b s t r a c t A new inequality is derived for the Bessel function of the first kind J ν (z), ν ∈ R, and a discussion of the consequent convergence is given for the generalized Kapteyn-type expan...
متن کاملTransplendent Models: Expansions Omitting a Type
We expand the notion of resplendency to theories of the kind T + p↑, where T is a first-order theory and p↑ expresses that the type p is omitted. We investigate two different formulations and prove necessary and sufficient conditions for countable recursively saturated models of PA. Some of the results in this paper can be found in one of the author’s doctoral thesis [3].
متن کاملA kinetic eikonal equation
We analyse the linear kinetic transport equation with a BGK relaxation operator. We study the large scale hyperbolic limit (t, x) → (t/ε, x/ε). We derive a new type of limiting Hamilton-Jacobi equation, which is analogous to the classical eikonal equation derived from the heat equation with small diffusivity. We prove well-posedness of the phase problem and convergence towards the viscosity sol...
متن کاملValidity of the Eikonal Approximation*
We summarize results on the reliability of the eikonal approximation in obtaining the high energy behavior of a two particle forward scattering amplitude. Reliability depends on the spin of the exchanged field. For scalar fields the eikonal fails at eighth order in perturbation theory, when it misses the leading behavior of the exchange-type diagrams. In a vector theory the eikonal gets the exc...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics
سال: 1978
ISSN: 0033-068X,1347-4081
DOI: 10.1143/ptp.59.320