Now showing items 1-20 of 27

    • A counterexample to a conjecture by De Giorgi in large dimensions 

      Pino Manresa, Manuel del; Kowalczyk, Michal; Wei, Juncheng (ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER, 2008-12)
      We consider the Allen–Cahn equation u +u 1− u2 =0 inRN. A celebrated conjecture by E. De Giorgi (1978) states that if u is a bounded solution to this problem such that ∂xNu>0, then the level sets {u=λ}, λ ∈R, ...
    • A counterexample to a conjecture by De Giorgi in large dimensions 

      Pino Manresa, Manuel del; Kowalczyk, Michal; Wei, Juncheng (ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER, 2008-12)
      We consider the Allen-Cahn equation Delta u + u(1 - u(2)) = 0 in R-N. A celebrated conjecture by E. De Giorgi (1978) states that if u is it bounded Solution to this problem Such that partial derivative(xN) u > 0, then ...
    • Critical points of the regular part of the harmonic Green function with Robin boundary condition 

      Dávila, Juan; Kowalczyk, Michal; Montenegro, Marcelo (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2008-09-01)
      In this paper we consider the Green function for the Laplacian in a smooth bounded domain Omega subset of R-N with Robin boundary condition partial derivative G(lambda)/partial derivative nu + lambda b(x)G(lambda) = 0, ...
    • Entire solutions to the inhomogeneous allen-cahn equation in R^2, with a transition on a noncompact curve 

      Zúñiga Munizaga, Andrés Jahir (Universidad de Chile, 2012)
      Este trabajo de memoria de título presenta un estudio de la ecuación de perturbación singular de Allen-Cahn con inhomogeneidad: \begin{equation}\ep^2\div\left(a(x)\cdot\nabla_{x}u(x)\right)+a(x)f(u(x))=0,\quad\text{ en ...
    • Estudio de Algunos Problemas Inversos y de Controlabilidad: Transmisión de Ondas y Transporte-Difusión 

      Mercado Saucedo, Alberto Carlos (Universidad de ChilePrograma Cybertesis, 2007)
    • Estudio de Soluciones Asintóticas de la Ecuación de Liouville con Condición de Borde Robin. 

      Topp Paredes, Erwin (Universidad de ChilePrograma Cybertesis, 2008)
    • Existence and asymptotic behavior of solutions to semilinear elliptic problems via reduction methods 

      Agudelo Rico, Óscar Iván (Universidad de Chile, 2012)
      Este trabajo se concentra principalmente en estudiar el método de reducción de Lyapunov-Schmidt y sus aplicaciones al estudio de existencia de soluciones a problemas semilineales elípticos. En particular, utilizamos ...
    • Ground States de Ecuaciones Elípticas No-Lineales: un Enfoque de Perturbaciones Singulares 

      Campos Serrano, Juan Francisco (Universidad de ChilePrograma Cybertesis, 2007)
      El objetivo de esta memoria es utilizar el método de perturbaciones singulares para probar existencia de ground states y soluciones singulares en ecuaciones elípticas no-lineales. .
    • A hybrid variational principle for the Keller-Segel system in R-2 

      Blanchet, Adrien; Carrillo, José Antonio; Kinderlehrer, David; Kowalczyk, Michal; Laurençot, Philippe; Lisini, Stefano (EDP Sciences, 2015)
      We construct weak global in time solutions to the classical Keller-Segel system describing cell movement by chemotaxis in two dimensions when the total mass is below the established critical value. Our construction takes ...
    • Improved interpolation inequalities on the sphere 

      Dolbeault, Jean; Esteban, María J.; Kowalczyk, Michal; Loss, Michael (American Institute Of Mathematical Sciences, 2014)
      This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, ...
    • THE JACOBI-TODA SYSTEM AND FOLIATED INTERFACES 

      Pino Manresa, Manuel del; Kowalczyk, Michal; Wei, Juncheng (2010-11)
      Let (M, ˜g) be an N-dimensional smooth (compact or noncompact) Riemannian manifold. We introduce the elliptic Jacobi-Toda system on (M, ˜g). We review various recent results on its role in the construction of solutions ...
    • Light-matter interaction induces a shadow vortex 

      Barboza, R.; Bortolozzo, U.; Clerc Gavilán, Marcel; Dávila Bonczos, Juan; Kowalczyk, Michal; Residori, S.; Vidal Henríquez, E. (Amer Physical Soc, 2016)
      By sending a light beam on a homeotropic nematic liquid-crystal cell subjected to a voltage with a photosensitive wall, a stable matter vortex can be induced at the center of the beam. When the applied voltage is decreased, ...
    • MULTIPLE-END SOLUTIONS TO THE ALLEN-CAHN EQUATION IN R2 

      Pino Manresa, 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 ...
    • Phase singularity dynamics in out of equilibrium anisotropic systems 

      Vidal Henríquez, Estefanía Carolina (Universidad de Chile, 2015)
      Esta tesis está enfocada en el estudio de singularidades de fase en el contexto de auto organización en sistemas fuera del equilibrio. Nuestra investigación estuvo focalizada en comprender el surgimiento de vórtices en una ...
    • Renormalized energy of interacting Ginzburg–Landau vortex filaments 

      Pino Manresa, Manuel del; Kowalczyk, Michal (London Mathematical Society, 2008)
      We consider the Ginzbug–Landau energy in a cylinder in R3, and a canonical approximation for critical points with an assembly of n 2 periodic vortex lines near the axis of the cylinder. We find a formula for the energy ...
    • Resonance and interior layers in an inhomogeneous phase transition model 

      Pino Manresa, Manuel del; Kowalczyk, Michal; Wei, Juncheng (SIAM PUBLICATIONS, 2006)
      We consider the problem epsilon(2)Delta u + (u - a(x))(1 - u(2)) = 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega, where Omega is a smooth and bounded domain in R-2, - 1 < a( x) < 1. ...
    • Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences 

      Dolbeault, Jean; Esteban, María J.; Kowalczyk, Michal; Loss, Michael (Springer, 2013)
      This paper is devoted to various considerations on a family of sharp interpolation inequalities on the sphere, which in dimension greater than 1 interpolate between Poincar´e, logarithmic Sobolev and critical Sobolev ...
    • Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice 

      Kowalczyk, Michal; Liu, Yong; Wei, Juncheng (Taylor & Francis, 2015)
      The Allen-Cahn equation - Delta u = u - u (3) in DOUBLE-STRUCK CAPITAL R-2 has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem -u '' =u - u (3). In this paper ...
    • Singular Limits in Liouville Type Equations With Exponential Neumann Data 

      Navarro Sepúlveda, Gustavo Estéban (Universidad de ChileCyberDocs, 2010)
      En este trabajo de memoria se demostró un teorema de existencia para la ecuación de Liouville con condición de borde no lineal: El primer paso en esta demostración consiste en la aproximación del problema original usando ...
    • Symmetry breaking and restoration in the ginzburg–landau model of nematic liquid crystals 

      Clerc Gavilán, Marcel; Kowalczyk, Michal; Smyrnelis, Panayotis (Springer, 2018-06)
      In this paper we study qualitative properties of global minimizers of the Ginzburg-Landau energy which describes light-matter interaction in the theory of nematic liquid crystals near the Freedericksz transition. This model ...