Symmetry and uniqueness of parabolic affine spheres.
Symmetry of solutions of semilinear elliptic problems
We study symmetry properties of least energy positive or nodal solutions of semilinear elliptic problems with Dirichlet or Neumann boundary conditions. The proof is based on symmetrizations in the spirit of Bartsch, Weth and Willem (J. Anal. Math., 2005) together with a strong maximum principle for quasi-continuous functions of Ancona and an intermediate value property for such functions.
Symmetry theorems via the continuous Steiner symmetrization.
The discrete maximum principle for Galerkin solutions of elliptic problems
This paper provides an equivalent characterization of the discrete maximum principle for Galerkin solutions of general linear elliptic problems. The characterization is formulated in terms of the discrete Green’s function and the elliptic projection of the boundary data. This general concept is applied to the analysis of the discrete maximum principle for the higher-order finite elements in one-dimension and to the lowest-order finite elements on simplices of arbitrary dimension. The paper surveys...
The evolution Darcy-Boussinesq system (a weak maximum principle and the uniqueness)
The maximum principle for equations with composite coefficients.
The Riccati differential equation and a diffusion-type equation.
The speed of propagation for KPP type problems. I: Periodic framework
This paper is devoted to some nonlinear propagation phenomena in periodic and more general domains, for reaction-diffusion equations with Kolmogorov–Petrovsky–Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a follow-up of the article [7]. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of the domain,...
Two Numerical Methods for the elliptic Monge-Ampère equation
The numerical solution of the elliptic Monge-Ampère Partial Differential Equation has been a subject of increasing interest recently [Glowinski, in 6th International Congress on Industrial and Applied Mathematics, ICIAM 07, Invited Lectures (2009) 155–192; Oliker and Prussner, Numer. Math.54 (1988) 271–293; Oberman, Discrete Contin. Dyn. Syst. Ser. B10 (2008) 221–238; Dean and Glowinski, in Partial differential equations, Comput. Methods Appl. Sci. 16 (2008) 43–63; Glowinski et al., Japan...
Two-sided Mullins-Sekerka flow does not preserve convexity.
Über die Existenz von unendlich vielen periodischen Lösungen einer einfachen Temperaturregelung.
Un Principio De Anti-Maximo Para Ecuaciones Parabolicas Periodicas.
Uniqueness and stability of solutions for a type of parabolic boundary value problem.
Uniqueness of the Solution of a Semilinear Boundary Value Problem.
Uniqueness of weak solution for nonlinear elliptic equations in divergence form.
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Variants on Alexandrov reflection principle and other applications of maximum principle
Varying domains in a general class of sublinear elliptic problems.
Viscosity solutions of elliptic partial differential equations.
Weak discrete maximum principles
We introduce weak discrete maximum principles for matrix equations associated with some elliptic problems. We also give an example on discrete maximum principles.