无界区域上具有奇异漂移项的非强制非线性椭圆方程的Dirichlet问题

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-10-24 DOI:10.1051/cocv/2023076

Patrizia Di Gironimo, Sara Monsurrò, Gabriella Zecca

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引用次数: 0

摘要

研究了无界区域上非强制一阶非线性椭圆方程的Dirichlet问题。当奇异漂移项在合适的函数空间中被函数控制时，我们得到了Stampacchia型的存在性、正则性和唯一性结果。主要的工具是一个弱极大值原理和一些由矛盾证明的先验估计。

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Dirichlet problem for noncoercive nonlinear elliptic equations with singular drift term in unbounded domains

In this paper we study a Dirichlet problem for noncoercive nonlinear elliptic equations with first order term in an unbounded domain. We obtain Stampacchia type existence, regularity and uniqueness results, when the singular drift term is controlled through a function in a suitable functional space, strictly containing Lebesgue one. The main tools are a weak maximum principle together with some a priori estimates proved by contradiction.

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Esaim-Control Optimisation and Calculus of Variations Mathematics-Computational Mathematics

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7.10%

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期刊介绍： ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations. Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines. Targeted topics include: in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory; in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis; in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.