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Viscosity solution is a notion of weak solution for a class of partial differential equations of Hamilton-Jacobi type. The range of applications of the notions of viscosity solution and Hamilton-Jacobi equations is enormous, including common class of partial differential equations such as evolutive problems and problems with boundary conditions ...
Camilli, Fabio, Prados, Emmanuel
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Controlled measure-valued martingales: A viscosity solution approach [PDF]
We consider a class of stochastic control problems where the state process is a probability measure-valued process satisfying an additional martingale condition on its dynamics, called measure-valued martingales (MVMs).
A. Cox +3 more
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Reflected generalized backward stochastic differential equations (BSDEs) with one discontinuous barrier are investigated when the noise is driven by a Brownian motion and an independent Poisson measure.
Mohammed Elhachemy, Mohamed El Otmani
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Mathematical study on the thickened interface model by viscosity solution of the level-set equation
The level-set approach extended for its viscosity solution is investigated to derive a relation to the conservation law of fluid phenomena and the phase-field approach based on the free energy theory.
Nobuyuki OSHIMA
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The Closed-Form Solution of an Extraction Model and Optimal Stopping Problems with Regime Switching
We aim to obtain by viscosity solution method the closed-form solution of a model concerning natural resource extraction in which a firm draws a schedule of when to stop the extraction.
Yong-Chao Zhang, Na Zhang, Qinglong Zhou
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Two-scale method for the Monge-Ampère equation: Convergence to the viscosity solution [PDF]
We propose a two-scale finite element method for the Monge-Amp\`ere equation with Dirichlet boundary condition in dimension $d\ge2$ and prove that it converges to the viscosity solution uniformly.
R. Nochetto +2 more
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$C^{1,\gamma}$ regularity for fully nonlinear elliptic equations on a convex polyhedron
In this note, we prove the boundary and global $C^{1,\gamma}$ regularity for viscosity solutions of fully nonlinear uniformly elliptic equations on a convex polyhedron by perturbation and iteration techniques.
Duan Wu, Pengcheng Niu
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Shape-from-shading (SFS) is an important method to reconstruct three-dimensional (3D) shape of a surface in photometry and computer vision. Lambertian surface reflectance and orthographic camera projection are two fundamental assumptions which generally ...
Guohui Wang, Hao Zheng
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Entry "Viscosity solution" of the Encyclopedia of Computer ...
CAMILLI, FABIO, E. Prados
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A double-phase eigenvalue problem with large exponents
In the present article, we consider a double-phase eigenvalue problem with large exponents. Let λ(pn,qn)1{\lambda }_{\left({p}_{n},{q}_{n})}^{1} be the first eigenvalues and un{u}_{n} be the first eigenfunctions, normalized by ‖un‖ℋn=1\Vert {u}_{n}{\Vert
Yu Lujuan
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