Comparison principle for dirichlet-type Hamilton-Jacobi equations and singular perturbations of degenerated elliptic equations

1990 ◽  
Vol 21 (1) ◽  
pp. 21-44 ◽  
Author(s):  
G. Barles ◽  
B. Perthame
Keyword(s):  
Comparison Principle ◽  
Singular Perturbations ◽  
Elliptic Equations ◽  
Dirichlet Type ◽  
Jacobi Equations

scholarly journals A comparison principle for Hamilton-Jacobi equations with discontinuous Hamiltonians

2011 ◽  
Vol 139 (05) ◽  
pp. 1777-1777 ◽  
Author(s):  
Yoshikazu Giga ◽  
Przemysław Górka ◽  
Piotr Rybka
Keyword(s):  
Comparison Principle ◽  
Jacobi Equations

scholarly journals Hamilton-Jacobi equations for optimal control on networks with entry or exit costs

2019 ◽  
Vol 25 ◽  
pp. 15 ◽  
Author(s):  
Manh Khang Dao
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Recent Work ◽  
Comparison Principle ◽  
Value Function ◽  
Exit Costs ◽  
Theory Of Optimal Control ◽  
New Feature ◽  
Jacobi Equations ◽  
The Value Function

We consider an optimal control on networks in the spirit of the works of Achdou et al. [NoDEA Nonlinear Differ. Equ. Appl. 20 (2013) 413–445] and Imbert et al. [ESAIM: COCV 19 (2013) 129–166]. The main new feature is that there are entry (or exit) costs at the edges of the network leading to a possible discontinuous value function. We characterize the value function as the unique viscosity solution of a new Hamilton-Jacobi system. The uniqueness is a consequence of a comparison principle for which we give two different proofs, one with arguments from the theory of optimal control inspired by Achdou et al. [ESAIM: COCV 21 (2015) 876–899] and one based on partial differential equations techniques inspired by a recent work of Lions and Souganidis [Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 27 (2016) 535–545].

scholarly journals A Comparison Principle for Some Types of Elliptic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Maria Emilia Amendola
Keyword(s):  
Comparison Principle ◽  
Elliptic Equations ◽  
Gradient Term ◽  
Fully Nonlinear ◽  
Viscosity Subsolution ◽  
Bmo Functions

In this paper a comparison principle between a continuous viscosity supersolution and a continuous viscosity subsolution is presented. The operator of interest is a fully nonlinear uniformly elliptic one with a gradient term which could be noncontinuous and grow like some BMO functions, as shown in the last section.

scholarly journals Comparison principle for some classes of nonlinear elliptic equations

2010 ◽  
Vol 249 (12) ◽  
pp. 3279-3290 ◽  
Author(s):  
Angelo Alvino ◽  
Maria Francesca Betta ◽  
Anna Mercaldo
Keyword(s):  
Comparison Principle ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic

scholarly journals Gradient estimates and comparison principle for some nonlinear elliptic equations

2015 ◽  
Vol 14 (3) ◽  
pp. 897-922 ◽  
Author(s):  
Maria Francesca Betta ◽  
Rosaria Di Nardo ◽  
Anna Mercaldo ◽  
Adamaria Perrotta
Keyword(s):  
Comparison Principle ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Gradient Estimates ◽  
Nonlinear Elliptic
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