Browsing by Author "cd575c79-dc74-4d4f-acbc-866068406907"

Now showing items 1-4 of 4

    • Ancient multiple-layer solutions to the Allen-Cahn equation 
      Pino, Manuel del; Gkikas, Konstantinos (Cambridge University Press, 2018)
      We consider the parabolic one-dimensional Allen-Cahn equation ut = uxx + u(1-u2), (x, t) R x (-0]. The steady state w(x) = tanh(x/2) connects, as a 'transition layer', the stable phases-1 and +1. We construct a solution u ...
    • Ancient shrinking spherical interfaces in the Allen-Cahn flow 
      Pino Manresa, Manuel del; Gkikas, Konstantinos T. (Elsevier Science BV, 2018)
      We consider the parabolic Allen Cahn equation in R-n, n >= 2, u(t) = Delta u + (1 - u(2))u in R-n x (-infinity, 0]. We construct an ancient radially symmetric solution u(x, t) with any given number k of transition ...
    • On the existence of weak solutions of semilinear elliptic equations and systems with Hardy potentials 
      Gkikas, Konstantinos T.; Nguyen, Phuoc Tai (Academic Press Inc., 2019)
      © 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>0. In this paper, we provide various necessary and sufficient conditions for the existence of weak ...
    • The spherical p-harmonic eigenvalue problem in non-smooth domains 
      Gkikas, Konstantinos T.; Veron, Laurent (Academic Press INC Elsevier Science, 2018)
      We prove the existence of p-harmonic functions under the form u(r, sigma) = r(-beta)omega(sigma) in any cone C-S generated by a spherical domain S and vanishing on partial derivative C-S. We prove the uniqueness of the ...