A natural approach to the asymptotic mean value property for the pp-Laplacian

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 the viscosity sense. Here, \mu_p(\ve,u)(x) is the $p$-mean value of $u$ on B_\ve(x) characterized as a unique minimizer of \inf_{\la\in\RR}\nr u-\la\nr_{L^p(B_\ve(x))}. This kind of asymptotic mean value property (AMVP) extends to the case $p=1$ previous (AMVP)'s obtained when \mu_p(\ve,u)(x) is replaced by other kinds of mean values. The natural definition of \mu_p(\ve,u)(x) makes sure that this is a monotonic and continuous (in the appropriate topology) functional of $u$. These two properties help to establish a fairly general proof of (AMVP), that can also be extended to the (normalized) parabolic $p$-Laplace equation.Comment: 19 pages, submitte

On the asymptotic behavior of unbounded radial solutions for semilinear parabolic problems involving critical Sobolev exponent

AbstractThis paper is concerned with a semilinear parabolic equation involving critical Sobolev exponent in a ball or in RN. The asymptotic behavior of unbounded, radially symmetric, nonnegative global solutions which do not decay to zero is given. The structure of the space of initial data is also discussed

Observational Constraint to the Minimum Flux Corona Model

The minimum flux corona model proposed by Hearn was compared with the observational data. The temperature derived from Hearn\u27s model is lower than that derived from X-ray observation for latetype main-sequence stars. In the solar coronal hole, Hearn\u27s minimum condition is not realized. The minimum flux corona model seems to be adequate only to the solar quiet region

肝細胞癌患者におけるGlypican-3陽性循環腫瘍細胞の臨床的意義

広島大学(Hiroshima University)博士(医学)Doctor of Philosophy in Medical Sciencedoctora