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Oscillation and jump inequalities for the polynomial ergodic averages along multi-dimensional subsets of primes
We prove the uniform oscillation and jump inequalities for the polynomial ergodic averages modeled over multi-dimensional subsets of primes. This is...
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Deep solution operators for variational inequalities via proximal neural networks
Following Bauschke and Combettes (Convex analysis and monotone operator theory in Hilbert spaces, Springer, Cham, 2017), we introduce ProxNet, a...
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Impulse Control of Conditional McKean–Vlasov Jump Diffusions
In this paper, we consider impulse control problems involving conditional McKean–Vlasov jump diffusions, with the common noise coming from the
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Variational inequalities for the commutators of rough operators with BMO functions
Starting with the relatively simple observation that the variational estimates of the commutators of the standard Calderón-Zygmund operators with the...
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Reflected Backward Stochastic Differential Equations Associated to Jump Markov Processes and Application to Partial Differential Equations
In this paper, we study a class of reflected backward stochastic differential equations (RBSDEs) driven by the compensated random measure associated...
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Isoperimetric Inequalities in Surfaces
In this chapter, we study isoperimetric inequalities in Riemannian surfaces. Firstly, we present Blaschke’s variational proof of the Gauss-Bonnet...
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Scalar, Multidimensional Variational Problems
Once we have established a solid functional-analytical foundation, we are ready to tackle multidimensional variational problems in which we pretend...
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Generalized Nash Equilibrium from a Robustness Perspective in Variational Analysis
Generalized Nash equilibrium is updated by a formulation in terms of extended-real-valued functions being minimized by the agents. Tools of...
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Maximum Principle for Stochastic Control System with Elephant Memory and Jump Diffusion
Motivated by a duopoly game problem, the authors study an optimal control problem where the system is driven by Brownian motion and Poisson point...
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Modulation Analysis of the Stochastic Camassa–Holm Equation with Pure Jump Noise
We study the stochastic Camassa–Holm equation with pure jump noise. We prove that if the initial condition of the solution is a solitary wave...
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New Variational Principles of Topological Pressures
We introduce three types of topological pressures and measure-theoretic pressures, present three variational principles between these...
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Splitting Method for the Variational Phase Transition Problem in Two-Phase Continuum Media
For the multi-dimensional variational phase transition problem of continuum mechanics we propose a method for splitting the problem into two parts...
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The Relaxed Stochastic Maximum Principle in Singular Optimal Control of Jump Diffusions
This paper deals with optimal control of systems driven by stochastic differential equations (SDEs), with controlled jumps, where the control...
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On Finite Volume Methods for a Navier–Stokes Variational Inequality
Finite volume methods are introduced to solve a class of variational inequality of the second kind, which is governed by the incompressible...
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One-Dimensional Variational Problems
This chapter is devoted to one of the most classical classes of variational problems, the one-dimensional case.
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A universal variational framework for parabolic equations and systems
We propose a variational approach to solve Cauchy problems for parabolic equations and systems independently of regularity theory for solutions. This...
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Existence and Uniqueness of Viscosity Solutions for Nonlinear Variational Inequalities Associated with Mixed Control
The author investigates the nonlinear parabolic variational inequality derived from the mixed stochastic control problem on finite horizon. Supposing...
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Multi-Dimensional Variational Problems
This short chapter establishes the bases of the multi-dimensional case, starting from the techniques which were described in the previous chapter for...