Ambrosio, Vincenzo Servadei, Raffaella
Published in
Fractional Calculus and Applied Analysis

In this paper we deal with the following fractional Kirchhoff problem M∬Rn×Rn|u(x)−u(y)|p|x−y|n+spdxdyp−1(−Δ)psu=f(x,u)+λ|u|r−2u in Ω,u=0 in Rn∖Ω. $$\begin{array}{} \displaystyle \left\{ {\begin{array}{l} \left[M\left(\displaystyle \iint_{\mathbb R^n\times \mathbb R^n} \frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}} dx dy\right)\right]^{p-1}(-\Delta)^{s}_{p}u =...

Liu, Zi Hong Pan, Gaopei Xu, Xiao Yan Sun, Kai Meng, Zi Yang
Published in
Proceedings of the National Academy of Sciences of the United States of America

Metallic quantum criticality is among the central themes in the understanding of correlated electronic systems, and converging results between analytical and numerical approaches are still under review. In this work, we develop a state-of-the-art large-scale quantum Monte Carlo simulation technique and systematically investigate the itinerant quant...

Slade, Gordon
Published in
Proceedings. Mathematical, Physical, and Engineering Sciences

The self-avoiding walk, and lattice spin systems such as the φ 4 model, are models of interest both in mathematics and in physics. Many of their important mathematical problems remain unsolved, particularly those involving critical exponents. We survey some of these problems, and report on recent advances in their mathematical understanding via a r...

holm-dahlin, sonja janas, sofie kreisel, andreas pomjakushina, ekaterina white, jonathan fennell, amy lefmann, kim

We investigated the antiferromagnetic phase transition in the frustrated and multiferroic hexagonal manganites h-YMnO 3 (YMO) and h-(Y 0 . 98 Eu 0 . 02 )MnO 3 (YEMO). Elastic neutron scattering was used to study, in detail, the phase transition in YMO and YEMO under zero pressure and in YMO under a hydrostatic pressure of 1.5 GPa. Under conditions ...

Coulon, Rémi Dal’Bo, Françoise Sambusetti, Andrea
Published in
Geometric and Functional Analysis

We prove a general version of the amenability conjecture in the unified setting of a Gromov hyperbolic group G acting properly cocompactly either on its Cayley graph, or on a CAT(-1)-space. Namely, for any subgroup H of G, we show that H is co-amenable in G if and only if their exponential growth rates (with respect to the prescribed action) coinci...

Bagyrov, Sh. G.
Published in
Mathematical Notes

The nonexistence of a global solution of the semilinear elliptic equation Δ2u − (C/|x|4)u − |x|σ|u|q = 0 in the exterior of a ball is studied. A sufficient condition for the nonexistence of a global solution is established. The proof is based on the test function method.

Matsuzaki, Katsuhiko

"Geometry and Analysis of Discrete Groups and Hyperbolic Spaces". June 22～26, 2015. edited by Michihiko Fujii, Nariya Kawazumi and Ken'ichi Ohshika. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. / Let G be a non-elementary discrete isometry group of the hyperbolic space or more generally a proper geo...

Il’yasov, Ya. Sh.
Published in
Computational Mathematics and Mathematical Physics

For semilinear elliptic equations −Δu = λ|u| p−2u−|u|q−2u, boundary value problems in bounded and unbounded domains are considered. In the plane of exponents p × q, the so-called curves of critical exponents are defined that divide this plane into domains with qualitatively different properties of the boundary value problems and the corresponding p...

Bagyrov, Sh. G. Gulieva, K. A.
Published in
Mathematical Notes

Wakasa, Kyouhei

"Harmonic Analysis and Nonlinear Partial Differential Equations". July 6～8, 2015. edited by Hideo Kubo and Mitsuru Sugimoto. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. / This note is a summary of the result in Wakasa [10]. We consider the semilinear wave equations with special scale invariant damp...