Some radii associated with polyharmonic equation, II
نویسندگان
چکیده
منابع مشابه
Removable Singularity of the Polyharmonic Equation
Abstract. Let x0 ∈ Ω ⊂ R, n ≥ 2, be a domain and let m ≥ 2. We will prove that a solution u of the polyharmonic equation ∆u = 0 in Ω \ {x0} has a removable singularity at x0 if and only if |∆u(x)| = o(|x − x0|) ∀k = 0, 1, 2, . . . , m − 1 as |x − x0| → 0 for n ≥ 3 and = o(log(|x−x0|)) ∀k = 0, 1, 2, . . . , m− 1 as |x−x0| → 0 for n = 2. For m ≥ 2 we will also prove that u has a removable singula...
متن کاملLarge Radial Solutions of a Polyharmonic Equation with Superlinear Growth
This paper concerns the equation ∆mu = |u|p, where m ∈ N, p ∈ (1,∞), and ∆ denotes the Laplace operator in RN, for some N ∈ N. Specifically, we are interested in the structure of the set L of all large radial solutions on the open unit ball B in RN . In the well-understood second-order case, the set L consists of exactly two solutions if the equation is subcritical, of exactly one solution if i...
متن کاملNeutron Star Masses, Radii and Equation of State
We are closing in on neutron stars both observationally and theoretically. Observationally, a number of masses (M) and a few radii (R) have been measured as well as a number of other properties. Theoretically, modern equation of states (EOS) are more reliable due to precision measurements of nucleon-nucleon interactions, detailed calculations of binding energies of light nuclei and nuclear matt...
متن کاملNeutron radii in nuclei and the neutron equation of state.
The root-mean-square radius for neutrons in nuclei is investigated in the Skyrme Hartree-Fock model. The main source of theoretical variation comes from the exchange part of the density-dependent interaction which can be related to a basic property of the neutron equation of state. A precise measurement of the neutron radius in 208Pb would place an important new constraint on the equation of st...
متن کاملPolyharmonic homogenization, rough polyharmonic splines and sparse super-localization
We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough (L∞) coefficients. Our method does not rely on concepts of ergodicity or scale-separation but on compactness properties of the solution space and a new variational approach to homogenization. The approximation space is generated by an interp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1971
ISSN: 0386-2194
DOI: 10.3792/pja/1195519970