Showing papers in "Journal D Analyse Mathematique in 1992"
328 citations
176 citations
TL;DR: In this article, the existence and uniqueness of a solutionu of−Lu+h|u| α-1u=f in some open domain ℝd, where L is a strongly elliptic operator, f is a nonnegative function, and α>1, under the assumption that ∂G is aC 2 compact hypersurface, lim x→∂G (dist(x, ∆G))2α/(α-1) f(x)=0, and lim x →∆G u(x) = ∞.
Abstract: We prove the existence and the uniqueness of a solutionu of−Lu+h|u| α-1u=f in some open domain ℝd, whereL is a strongly elliptic operator,f a nonnegative function, and α>1, under the assumption that ∂G is aC 2 compact hypersurface, lim x→∂G (dist(x, ∂G))2α/(α-1) f(x)=0, and lim x→∂G u(x)=∞.
158 citations
TL;DR: In this paper, the Schrodinger equation is considered and the following estimates are proved: (A) IfV≡0 then for any 0≤α 1/2, {fx25-3} and (B) If |V(x)|≤C(1+|x|2)−1−δ, δ>0, then (if 0 is neither an eigenvalue nor a resonance of −Δ+V), {FX25-4}.
Abstract: Consider the Schrodinger equation {fx25-1}. The following estimates are proved: (A) IfV≡0 then for any 0≤α 1/2, {fx25-3} (B) If |V(x)|≤C(1+|x|2)−1−δ, δ>0, then (if 0 is neither an eigenvalue nor a resonance of −Δ+V), {fx25-4}.
149 citations
73 citations
70 citations
62 citations
TL;DR: In this article, the authors established a relationship between the local smoothing properties of evolution equations and boundary control theory, which extends to hyperbolic equations, as well as equations of the Schrodinger type.
Abstract: We establish a relationship between the local smoothing properties of evolution equations and boundary control theory. This relationship extends to hyperbolic equations, as well as equations of the Schrodinger type.
40 citations
TL;DR: In this paper, the existence and uniqueness of singular solutions for equations of the formu 1=div(|Du|p−2 Du)-φu, with initial datau(x, 0)=0 forx⇑0.
Abstract: We consider the existence and uniqueness of singular solutions for equations of the formu 1=div(|Du|p−2 Du)-φu), with initial datau(x, 0)=0 forx⇑0. The function ϕ is a nondecreasing real function such that ϕ(0)=0 andp>2.
39 citations
TL;DR: In this article, a perturbative renormalization of perturbation expansions for quasi-periodic orbits in Hamiltonian mechanics is described, followed by the derivation of the formal ground state energy density of a Fermion system.
Abstract: We attempt to give apedagogical introduction to perturbative renormalization. Our approach is to first describe, following Linstedt and Poincare, the renormalization of formal perturbation expansions for quasi-periodic orbits in Hamiltonian mechanics. We then discuss, following [FT1, FT2], the renormalization of the formal ground state energy density of a many Fermion system. The construction of formal quasi-periodic orbits is carried out in detail to provide a relatively simple model for the considerably more involved, and perhaps less familiar, perturbative analysis of a field theory.
22 citations
TL;DR: In this article, the authors extended the theory from [K2] to some weakly coupled parabolic systems of PDE which generate Markov processes with switching at random times between a finite number of diffusion processes.
Abstract: This paper extends the theory from [K2] to some weakly coupled parabolic systems of PDE which generate Markov processes with switching at random times between a finite number of diffusion processes.
TL;DR: In this article, the Schrodinger operator with the Neumann boundary condition on a sphere is studied and the resolvent equation for the Schroeder operator with an interface condition on the sphere is discussed.
Abstract: We study basic properties of the Schrodinger operatorH with an interface condition on a sphere which allows gaps in values but requires continuity of normal derivatives.H can be regarded as a perturbation ofH N, the Schrodinger operator with the Neumann boundary condition on the sphere. The resolvent equation forH andH N is also discussed.
TL;DR: In this paper, the authors show how to realize a variety of discrete maps as time-one evaluations of integrable Hamiltonian flows and show that these maps can be realized as discrete maps.
Abstract: We show how to realize a variety of discrete maps as time-one evaluations of integrable Hamiltonian flows.
TL;DR: In this paper, a differential geometric interpetation of adiabatic charge transport in quantum mechanics is described, which involves the study of afamily of Schrodinger operators.
Abstract: This is abrief and informal introduction to a differential geometric interpetation of adiabatic charge transport in quantum mechanics. It involves the study of afamily of Schrodinger operators. For compact multiply connected surfaces the charge transported around the “holes” is related to the first Chern character of spectral bundles. For noncompact surfaces the charge transported to infinity is related to the index of a certain Fredholm operator which involves the comparison of appropriate spectral projections. There are also relations to Connes noncommutative differential geometry. Simple examples are given.