Laura Abatangelo,Veronica Felli,Corentin Léna
Laura Abatangelo
We consider Aharonov-Bohm operators with two poles and prove sharp asymptotics for simple eigenvalues as the poles collapse at an interior point out of nodal lines of the limit eigenfunction. ...
Monotonicity and Symmetry of Nonnegative Solutions to -Δ u=f(u) in Half-Planes and Strips [0.03%]
半平面和带形区域上−Δu = f(u)的非负解的单调性和对称性
Alberto Farina,Berardino Sciunzi
Alberto Farina
We consider nonnegative solutions to -Δ⁢u=f⁢(u) in half-planes and strips, under zero Dirichlet boundary condition. Exploiting a rotating and sliding line technique, we prove symmetry and monotonicity properties of the solu...
Optimal Functional Inequalities for Fractional Operators on the Sphere and Applications [0.03%]
球面上分数阶算子的最佳函数不等式及其应用
Jean Dolbeault,An Zhang
Jean Dolbeault
This paper is devoted to the family of optimal functional inequalities on the n-dimensional sphere 𝕊 n , namely ∥ F ∥ L q ⁢ ( 𝕊 n ) 2 - ∥ F ∥ L 2 ⁢ ( 𝕊 n ) 2 q - 2 Ͱ...
Refined Regularity of the Blow-Up Set Linked to Refined Asymptotic Behavior for the Semilinear Heat Equation [0.03%]
与半线性热方程奇点集精细正则性相联系的精细渐近行为
Tej-Eddine Ghoul,Van Tien Nguyen,Hatem Zaag
Tej-Eddine Ghoul
We consider u ⁢ ( x , t ) , a solution of ∂ t ⁡ u = Δ ⁢ u + | u | p - 1 ⁢ u which blows up at some time T > 0 , where u : ℝ N × [ 0 , T ) → ℝ , p > 1 and ( N - 2 ) &...