Zobrazeno 1 - 10
of 62
pro vyhledávání: '"Wadade, Hidemitsu"'
In a recent paper, the last three authors showed that a game-theoretic $p$-harmonic function $v$ is characterized by an asymptotic mean value property with respect to a kind of mean value $\nu_p^r[v](x)$ defined variationally on balls $B_r(x)$. In th
Externí odkaz:
http://arxiv.org/abs/2101.02662
Autor:
Ishiwata, Michinori, Wadade, Hidemitsu
In this paper, we consider a maximizing problem associated with the Sobolev type embedding on the space of bounded variation. We show that, although the maximizing problem suffers from both of the non-compactness of vanishing and concentrating phenom
Externí odkaz:
http://arxiv.org/abs/1905.07759
In this paper, we study the existence and non-existence of maximizers for the Moser-Trudinger type inequalities in $\Bbb R^N$ of the form \[ D_{N,\alpha}(a,b):= \sup_{u\in W^{1,N}(\Bbb R^N),\,\|\nabla u\|_{L^N(\Bbb R^N)}^a+\|u\|_{L^N(\Bbb R^N)}^b=1}
Externí odkaz:
http://arxiv.org/abs/1801.03271
We study the Rellich inequalities in the framework of equalities. We present equalities which imply the Rellich inequalities by dropping remainders. This provides a simple and direct understanding of the Rellich inequalities as well as the nonexisten
Externí odkaz:
http://arxiv.org/abs/1611.03625
We study the Hardy type inequalities in the framework of equalities. We present equalities which immediately imply Hardy type inequalities by dropping the remainder term. Simultaneously we give a characterization of the class of functions which makes
Externí odkaz:
http://arxiv.org/abs/1611.03580
Let $1\le p\le\infty$. We show that a function $u\in C(\mathbb R^N)$ is a viscosity solution to the normalized $p$-Laplace equation $\Delta_p^n u(x)=0$ if and only if the asymptotic formula $$ u(x)=\mu_p(\ve,u)(x)+o(\ve^2) $$ holds as $\ve\to 0$ in t
Externí odkaz:
http://arxiv.org/abs/1604.00520
On the sharp constant for the weighted Trudinger–Moser type inequality of the scaling invariant form
Publikováno v:
In Annales de l'Institut Henri Poincaré / Analyse non linéaire March-April 2014 31(2):297-314
Publikováno v:
Indiana University Mathematics Journal, 2006 Jan 01. 55(6), 1951-1974.
Externí odkaz:
https://www.jstor.org/stable/24902674
Akademický článek
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Publikováno v:
In Nonlinear Analysis 2010 73(6):1747-1766