In this paper, we study the existence of positive entire large radial solutions to the nonlinear elliptic system with gradient terms { div(|∇u|p−2∇u) + |∇u| = m(|x|)f1(v)f2(u), x ∈ RN div(|∇v|q−2∇v) + |∇v| = n(|x|)g1(v)g2(u), x ∈ RN (1) The nonlinearities fi, gi (i = 1, 2) are positive and continuous, while the potentials m, n are continuous and certain growth condition. We give some simple con...

We prove a strong approximation result for functions u ∈ W 1,∞(Ω \ J), where J is the union of finitely many Lipschitz graphs satisfying some further technical assumptions. We approximate J by a polyhedral set in such a manner that a regularisation term η(Div u), (i = 0, 1, 2, . . .), is convergent. The boundedness of this regularisation functional itself, introduced in [T. Valkonen: “Transport...

(1.1) gj(x) := x− yj |x− yj |n , x ∈ Rn \ {yj}. Let Hs,p denote the usual scale of Lp-Sobolev spaces, and denote by div and Div the divergence of 1-tensors (i.e., vector fields) and 2-tensors, respectively. Given a divergence-free vector field u on Ω, possessing a certain regularity, e.g., u ∈ Hs,p(Ω), we want to investigate two closely related problems. One is to extend u to a divergence-free ...

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>The rapid spread of the Covid-19 virus has had an impact on various aspects life, such as economy, education, and socialisation. One social distancing policies in field education is application distance learning at preschool, primary school, secondary special college levels. Its i...

Striatal neurons were cultured from the fetal mouse brain and maintained in serum-free medium for 14-21 days in vitro (DIV). Pretreatment of the culture dishes successively with a polycation followed by fetal calf serum resulted in rapid neuron attachment and neurite proliferation. After 9-10 DIV, electron microscope observations revealed the presence of vesicles in axon terminals forming matur...