Vanishing viscosity solutions for conservation laws with regulated flux
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DOI: 10.1016/j.jde.2018.07.044
Abstract: Abstract In this paper we introduce a concept of “regulated function” v ( t , x ) of two variables, which reduces to the classical definition when v is independent of t. We then consider… read more here.
Keywords: vanishing viscosity; conservation laws; viscosity; viscosity solutions ... See more keywords
On existence and uniqueness of viscosity solutions to obstacle problems for a class of second order partial differential equations
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DOI: 10.1016/j.jmaa.2019.02.057
Abstract: Abstract We prove the existence and uniqueness of the viscosity solutions to the obstacle problems for second order differential partial equations under some conditions. As applications, we show some existence and uniqueness theorems of the… read more here.
Keywords: uniqueness viscosity; solutions obstacle; viscosity solutions; existence uniqueness ... See more keywords
Symmetry results for viscosity solutions of fully nonlinear equations in annular and exterior domains
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DOI: 10.1016/j.jmaa.2019.123776
Abstract: Abstract In this paper, we prove the symmetry and monotonicity results of viscosity solutions for fully nonlinear elliptic equations F ( D 2 u , D u , u , x ) = 0 and… read more here.
Keywords: fully nonlinear; exterior domains; solutions fully; equations annular ... See more keywords
Delay optimal control and viscosity solutions to associated Hamilton–Jacobi–Bellman equations
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DOI: 10.1080/00207179.2018.1436769
Abstract: ABSTRACT In this article, optimal control problems of differential equations with delays are investigated for which the associated Hamilton–Jacobi–Bellman (HJB) equations are nonlinear partial differential equations with delays. This type of HJB equation has not… read more here.
Keywords: hamilton jacobi; control; jacobi bellman; associated hamilton ... See more keywords
Weighted Lorentz and Lorentz–Morrey estimates to viscosity solutions of fully nonlinear elliptic equations
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DOI: 10.1080/17476933.2017.1357707
Abstract: Abstract We prove a global weighted Lorentz and Lorentz–Morrey estimates of the viscosity solutions to the Dirichlet problem for fully nonlinear elliptic equation defined in a bounded domain. The oscillation of nonlinearity F with respect… read more here.
Keywords: estimates viscosity; morrey estimates; lorentz morrey; weighted lorentz ... See more keywords
Crandall–Lions viscosity solutions for path-dependent PDEs: The case of heat equation
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DOI: 10.3150/21-bej1353
Abstract: We address our interest to the development of a theory of viscosity solutions a la Crandall-Lions for path-dependent partial differential equations (PDEs), namely PDEs in the space of continuous paths C([0, T ]; R^d). Path-dependent… read more here.
Keywords: crandall lions; path dependent; equation; dependent pdes ... See more keywords