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2009, Volume 8, Issue 4: 1291-1302. Doi: 10.3934/cpaa.2009.8.1291
This issue Previous Article Multiple solutions for a critical nonhomogeneous elliptic problem in domains with small holes Next Article Blowup and global existence of the nonlinear Schrödinger equations with multiple potentials

Systems of convex Hamilton-Jacobi equations with implicit obstacles and the obstacle problem

  • 1.

    Sez. di Matematica per I'Ingegneria, Dip. di Matematica Pura e Applicata, Università dell'Aquila, 67040 Roio Poggio (AQ)

  • 2.

    Dipartimento Metodi e Modelli Matematici, per le Scienze Applicate, Università di Roma "La Sapienza", Via A. Scarpa 16, 00161 Roma

  • 3.

    Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka 814-0180

Received:  May 2008
Revised:  December 2008
Published:  July 2009
Abstract / Introduction Related Papers Cited by
    Abstract
  • Aim of this paper is to show that some of the results in the weak KAM theory for $1^{s t}$ order convex Hamilton-Jacobi equations (see [11], [13]) can be extended to systems of convex Hamilton-Jacobi equations with implicit obstacles and to the obstacle problem. We obtain two results: a comparison theorem for systems lacking strict monotonicity; a representation formula for the obstacle problem involving the distance function associated to the Hamiltonian of the equation.
    Mathematics Subject Classification: Primary: 49L25; Secondary: 35F30, 35B25.

    Citation:
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