• End-to-end construction for the Allen–Cahn equation in the plane 

      Kowalczyk, Michał; Liu, Yong; Pacard, Frank; Wei, Juncheng (Springer, 2015)
      In this paper, we construct a wealth of bounded, entire solutions of the Allen–Cahn equation in the plane. The asymptotic behavior at infinity of these solutions is determined by 2L half affine lines, in the sense that, ...
    • MULTIPLE-END SOLUTIONS TO THE ALLEN-CAHN EQUATION IN R2 

      Pino, Manuel del; Kowalczyk, Michal; Pacard, Frank; Wei, Juncheng (2010)
      We construct a new class of entire solutions for the Allen-Cahn equation u + (1 􀀀 u2)u = 0, in R2( C). Given k 1, we nd a family of solutions whose zero level sets are, away from a compact set, asymptotic to 2k ...
    • Serrin’s overdetermined problem and constant mean curvature surfaces 

      Pino Manresa, Manuel del; Pacard, Frank; Wei, Juncheng (Duke Univ Press, 2015)
      For all N >= 9, we find smooth entire epigraphs in R-N, namely, smooth domains of the form Omega := {x is an element of R-N broken vertical bar X-N broken vertical bar > F(X-1, . . . , X-N-1)}, which are not half-spaces ...
    • The Toda system and multiple-end solutions of autonomous planar elliptic problems 

      Pino, Manuel del; Kowalczyk, Michal; Pacard, Frank; Wei, Juncheng (2010)
      We construct a new class of positive solutions for the classical elliptic problem ¢u ¡ u + up = 0; p > 2; in R2: We establish a deep relation between them and the following Toda system c2f00 j = efj¡1¡fj ¡ efj¡fj+1 in ...