We study the boundary behavior of positive functions u satisfying (E) - Delta u-kappa/d(2)(x)u+g(u) = 0 in a bounded domain ohm of R-N, where 0 < kappa <= 1/4, g is a continuous nondecreasing function and d(.) is the ...

In this paper we study the best constant in the Sobolev trace embedding H1 (Ω) → Lq(∂Ω) in a bounded smooth domain for 1 < q ≤ 2+ = 2(N - 1)/(N - 2), that is, critical or subcritical q. First, we consider a domain with ...

In this paper we study homogenisation problems for Sobolev trace embedding H1(Ω) ↪ Lq(∂Ω) in a bounded smooth domain. When q = 2 this leads to a Steklov-like eigenvalue problem. We deal with the best constant of the Sobolev ...

In this paper we study homogenization problems for the best constant for the Sobolev trace embedding W1, p (Ω) {right arrow, hooked} Lq (∂ Ω) in a bounded smooth domain when the boundary is perturbed by adding an oscillation. ...

We consider symmetry properties of minimizers in the variational characterization of the best constant in the trace inequality C∥u∥^p_L^q(∂B_ρ) ≤∥u∥^p_W1,p(Bρ) in the ball Bρ of radius ρ. When p is fixed minimizers in this ...

Classical (trace) conditioning is a specific variant of associative learning in which a neutral stimulus leads to the subsequent prediction of an emotionally charged or noxious stimulus after a temporal gap. When conditioning ...

In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient ||u||_{1,p} / ||u||_{p} among functions that vanish in a set contained on the boundary of the domain of given boundary measure. We prove ...

© 2018 Elsevier Inc.Let Ω⊂RN (N≥3) be a bounded C2 domain and δ(x)=dist(x,∂Ω). Put Lμ=Δ+[Formula presented] with μ&gt;0. In this paper, we provide various necessary and sufficient conditions for the existence of weak ...