Universal approximation by translates of fundamental solutions of elliptic equations
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Vassili Nestoridis
Abstract
In the present work, we investigate the approximability of solutions of elliptic partial differential equations in a bounded domain Ω by universal series of translates of fundamental solutions of the underlying partial differential operator. The singularities of the fundamental solutions lie on a prescribed surface outside of –Ω, known as the pseudo-boundary. The domains under consideration satisfy a rather mild boundary regularity requirement, namely, the segment condition. We study approximations with respect to the norms of the spaces Cℓ(–Ω)and we establish the existence of universal series. Analogous results are obtainable with respect to the norms of Hölder spaces Cℓ,ν(–Ω). The sequence a = {an}n ∈ ℕ of coefficients of the universal series may be chosen in ∩ p > 1lp(ℕ) but it can not be chosen in l1(ℕ).
© by Oldenbourg Wissenschaftsverlag, Nicosia, Germany
Articles in the same Issue
- A Brunn–Minkowski inequality for a Finsler–Laplacian
- Irrationality of certain infinite series II
- Elastic catenoids
- On the distribution of zeros of monic polynomials with a given uniform norm on a quasidisk
- Universal approximation by translates of fundamental solutions of elliptic equations
- Exclusion of boundary branch points for minimal surfaces
- On the uniform convergence of double sine integrals over –ℝ 2+
Articles in the same Issue
- A Brunn–Minkowski inequality for a Finsler–Laplacian
- Irrationality of certain infinite series II
- Elastic catenoids
- On the distribution of zeros of monic polynomials with a given uniform norm on a quasidisk
- Universal approximation by translates of fundamental solutions of elliptic equations
- Exclusion of boundary branch points for minimal surfaces
- On the uniform convergence of double sine integrals over –ℝ 2+
