A. Tachikawa

most citedRegularity for minimizers for functionals of double phase with variable exponents

311 citations · 314 across the 7 of their papers we have counts for

collaborators

7 papers

math.AP2020

Energy estimates of harmonic maps between Riemannian manifolds

M. A. Ragusa, A. Tachikawa

Let $Ω \subset R^{n},$ $n \geq 3,$ be a bounded open set, $x = (x_{1}, x_{2}, \dots, x_{n})$ a generic point which belongs to $Ω,$ $u : Ω \to R^{N},$ $N > 1,$ and $D u = (D_{α} u^{i})$ , $D_α= \pa…

math.AP2020

Regularity of minimizers of some variational integrals with discontinuity

Maria Alessandra Ragusa, Atsushi Tachikawa

We prove regularity properties in the vector valued case for minimizers of variational integrals of the form $A (u) = \int_{Ω} A (x, u, D u) d x$ where the integrand $A (x, u, D u)$ is not ne…

math.AP2020★ 2 cited

Interior estimates in Campanato spaces related to quadratic functionals

M. A. Ragusa, A. Tachikawa

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

math.AP2020★ 311 cited

Regularity for minimizers for functionals of double phase with variable exponents

M. A. Ragusa, A. Tachikawa

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 Col…

math.AP2011

$C^{1, α}$ -Regularity of energy minimizing maps from a 2-dimentional domain into a Finsler space

Atsushi Tachikawa

We show $C^{1, α}$ -regularity for energy minimizing maps from a 2-dimensional Riemannian manifold into a Finsler space $(R^{n}, F)$ with a Finsler structure $F (u, X)$ .

math.AP2011★ 1 cited

Partial regularity of $p (x)$ -harmonic maps

Maria Alessandra Ragusa, Atsushi Tachikawa, Hiroshi Takabayashi

Let $(g^{α β} (x))$ and $(h_{ij} (u))$ be uniformly elliptic symmetric matrices, and assume that $h_{ij} (u)$ and $p (x) (\geq 2)$ are sufficiently smooth. We prove partial regula…

Energy estimates of harmonic maps between Riemannian manifolds

Regularity of minimizers of some variational integrals with discontinuity

Interior estimates in Campanato spaces related to quadratic functionals

Regularity for minimizers for functionals of double phase with variable exponents

C1,α-Regularity of energy minimizing maps from a 2-dimentional domain into a Finsler space

Partial regularity of p(x)-harmonic maps

$C^{1, α}$ -Regularity of energy minimizing maps from a 2-dimentional domain into a Finsler space

Partial regularity of $p (x)$ -harmonic maps