Mean-Field Stochastic Control with Elephant Memory in Finite and Infinite Time Horizon
, 2019 Our purpose of this paper is to study stochastic control problem for systems driven by mean-field stochastic differential equations with elephant memory, in the sense that the system (like the elephants) never forgets its history.
Agram, Nacira, Øksendal, Bernt
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Nonlinear maximum principles for dissipative linear nonlocal operators and applications
, 2011 We obtain a family of nonlinear maximum principles for linear dissipative nonlocal operators, that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of global regularity for critical SQG and critical d ...
Constantin, Peter, Vicol, Vlad
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Remarks on comparison principles for -Laplacian with extension to -Laplacian
Bulletin of Mathematical SciencesOur purpose is to generalize some recent comparison principles for operators driven by [Formula: see text]-Laplacian to a wide class of quasilinear equations including [Formula: see text]-Laplacian.
Ahmed Mohammed, Antonio Vitolo
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Maximum principles for boundary-degenerate second-order linear elliptic differential operators
, 2013 We prove weak and strong maximum principles, including a Hopf lemma, for smooth subsolutions to equations defined by linear, second-order, partial differential operators whose principal symbols vanish along a portion of the domain boundary.
Feehan, Paul M. N.
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The effects of nonlinear perturbation terms on comparison principles for the -Laplacian
Bulletin of Mathematical SciencesIn this paper, we investigate various comparison principles for quasilinear elliptic equations of [Formula: see text]-Laplace type with lower-order terms that depend on the solution and its gradient.
Ahmed Mohammed, Antonio Vitolo
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Some maximum principles for solutions of a class of partial differential equations in Ω⊂ℝn
International Journal of Mathematics and Mathematical Sciences, 2000 We find maximum principles for solutions of semilinear elliptic partial differential equations of the forms: (1) Δ2u+αf(u)=0, α∈ℝ+ and (2) ΔΔu+α(Δu)k+gu=0, α≤0 in some region Ω⊂ℝn.
Mohammad Mujalli Al-Mahameed
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The maximum principle for equations with composite coefficients
Electronic Journal of Differential Equations, 2000 It is well-known that the maximum of the solution of a linear elliptic equation can be estimated in terms of the boundary data provided the coefficient of the gradient term is either integrable to an appropriate power or blows up like a small negative ...
Gary M. Lieberman
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Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation
Discrete Dynamics in Nature and Society, 2015 We study reaction-diffusion equations with a general reaction function f on one-dimensional lattices with continuous or discrete time ux′ (or Δtux)=k(ux-1-2ux+ux+1)+f(ux), x∈Z.
Petr Stehlík, Jonáš Volek
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Well-posedness and maximum principles for lattice reaction-diffusion equations
Advances in Nonlinear Analysis, 2017 Existence, uniqueness and continuous dependence results together with maximum principles represent key tools in the analysis of lattice reaction-diffusion equations.
Slavík Antonín +2 more
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Strong maximum principles for implicit parabolic functional-differential problems together with nonlocal inequalities with functionals [PDF]
Opuscula Mathematica, 2009 The aim of the paper is to give strong maximum principles for implicit parabolic functional-differential problems together with nonlocal inequalities with functionals in relatively arbitrary \((n+1)\)-dimensional time-space sets more general than the ...
Ludwik Byszewski
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