arXiv subjects

A. Tachikawa

Publications and source records attributed to A. Tachikawa.

3 recordsLinked to original sources

arXiv2020

Energy estimates of harmonic maps between Riemannian manifolds

Let $Ω\subset {R}^n,$ $n \geq 3,$ be a bounded open set, $x=(x_1,x_2,\ldots,x_n)$ a generic point which belongs to $Ω,$ $u \colon Ω\to {R}^N ,$ $N>1,$ and $ Du=(D_αu^i)$, $D_α= \partial/\partial x_α, $ $α=1,\ldots,n,\,$ $i=1,\ldots,N .\,$ Main goal is the study of regularity of the minima of nondifferentiable functionals $$ {\cal F} \,=\, \int_ΩF(x,u,Du) dx. $$ having the integrand function different shapes of smoothness. The method is based on the use some majorizations for the functional, rather than the well known Euler equation associated to it.

math.AP↗

arXiv2020

Interior estimates in Campanato spaces related to quadratic functionals

In this paper we obtain interior estimates in Campanato spaces for the derivatives of the minimizers of quadratic functionals.

math.AP↗

arXiv2020

Regularity for minimizers for functionals of double phase with variable exponents

The functionals of double phase type \[ \mathcal{H} (u):= \int \left(|Du|^{p} + a(x)|Du|^{q} \right) dx, ( q > p > 1, a(x)\geq 0) \] are introduced in the epoch-making paper by Colombo-Mingione for constants $p$ and $q$, and investigated by them and Baroni. They obtained sharp regularity results for minimizers of such functionals. In this paper we treat the case that the exponents are functions of $x$ and partly generalize their regularity results.

math.AP↗