Piecewise Constant Subsolutions for the Muskat Problem [PDF]
Communications in Mathematical Physics, 2018 We show the existence of infinitely many admissible weak solutions for the incompressible porous media equations for all Muskat-type initial data with $C^{3,α}$-regularity of the interface in the unstable regime and for all non-horizontal data with $C^{3,α}$-regularity in the stable regime.
Clemens Förster, László Székelyhidi
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Importance Sampling for a Simple Markovian Intensity Model Using Subsolutions [PDF]
ACM Transactions on Modeling and Computer Simulation, 2022 This article considers importance sampling for estimation of rare-event probabilities in a specific collection of Markovian jump processes used for, e.g., modeling of credit risk. Previous attempts at designing importance sampling algorithms have resulted in poor performance and the main contribution of the article is the design of efficient importance
Boualem Djehiche +2 more
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Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in the annulus [PDF]
Opuscula Mathematica, 2015 In this paper, we establish existence and asymptotic behavior of a positive classical solution to the following semilinear boundary value problem: \[-\Delta u=q(x)u^{\sigma }\;\text{in}\;\Omega,\quad u_{|\partial\Omega}=0.\] Here \(\Omega\) is an annulus
Safa Dridi, Bilel Khamessi
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Regularization of Subsolutions in Discrete Weak KAM Theory [PDF]
Canadian Journal of Mathematics, 2013 AbstractWe expose different methods of regularizations of subsolutions in the context of discrete weak KAM theory that allow us to prove the existence and the density of C1,1 subsolutions. Moreover, these subsolutions can be made strict and smooth outside of the Aubry set.
Bernard, Patrick, Zavidovique, Maxime
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Weak subsolutions to complex Monge–Ampère equations [PDF]
Journal of the Mathematical Society of Japan, 2019 We compare various notions of weak subsolutions to degenerate complex Monge-Ampère equations, showing that they all coincide. This allows us to give an alternative proof of mixed Monge-Ampère inequalities due to Kolodziej and Dinew.
Guedj, Vincent +2 more
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An Algorithm to Construct Subsolutions of Convex Optimal Control Problems
SIAM Journal on Control and Optimization, 2022 37 pages, 3 figures, 5 tables.
Gianmarco Bet, Markus Fischer
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Combined effects in nonlinear singular elliptic problems in a bounded domain
Advances in Nonlinear Analysis, 2012 We establish an existence result of positive solutions to the following boundary value problem:
Chemmam Rym +3 more
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Optimal consumption problem in the Vasicek model [PDF]
Opuscula Mathematica, 2015 We consider the problem of an optimal consumption strategy on the infinite time horizon based on the hyperbolic absolute risk aversion utility when the interest rate is an Ornstein-Uhlenbeck process.
Jakub Trybuła
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Existence and asymptotic behavior of ground state solutions of semilinear elliptic system
Advances in Nonlinear Analysis, 2017 In this article, we take up the existence and the asymptotic behavior of entire bounded positive solutions to the following semilinear elliptic system:
Mâagli Habib +2 more
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Boundary behaviors for linear systems of subsolutions of the stationary Schrödinger equation
Journal of Inequalities and Applications, 2016 This paper investigates the boundary behaviors for linear systems of subsolutions of the stationary Schrödinger equation, which contain unstable subsystems.
Zongcai Jiang, Francisco Marco Usó
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