Kouta Sekine

activity

20142019

most citedSharp numerical inclusion of the best constant for embedding

H_{0}^{1} (Ω) ↪ L^{p} (Ω)

on bounded convex domain

11 citations · 21 across the 7 of their papers we have counts for

collaborators

Showing 2016Show all

3 papers · 1 filter

math.FA2016

Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains

Makoto Mizuguchi, Kazuaki Tanaka, Kouta Sekine +1

This paper is concerned with an explicit value of the embedding constant from $W^{1, q} (Ω)$ to $L^{p} (Ω)$ for a bounded domain $Ω \subset R^{N} (N \in N)$ , where $1\leq…

math.NA2016

Numerical verification method for positiveness of solutions to elliptic equations

Kazuaki Tanaka, Kouta Sekine, Shin'ichi Oishi

In this paper, we propose a numerical method for verifying the positiveness of solutions to semilinear elliptic equations. We provide a sufficient condition for a solution to an el…

math.NA2016

Rigorous numerical enclosures for positive solutions of Lane-Emden's equation with sub-square exponents

Kazuaki Tanaka, Michael Plum, Kouta Sekine +2

The purpose of this paper is to obtain rigorous numerical enclosures for solutions of Lane-Emden's equation $- Δ u = ∣ u ∣^{p - 1} u$ with homogeneous Dirichlet boundary conditions. We pro…