具有p(·)-增长的自由不连续问题的极小解的规律性

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS

Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-03-03 DOI:10.1051/cocv/2023062

C. Leone, G. Scilla, Francesco Solombrino, A. Verde

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引用次数: 2

摘要

摘要在变指数p(x)具有log-Ho¨lder连续性的假设下，证明了在变指数有界变函数空间SBV p(·)上定义的自由不连续能量的一个正则性结果。我们的分析扩展了非标准生长情况下一类自由不连续问题的极小值的正则性理论。这可以看作是论文[24]的后续，处理常数指数。

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Regularity of minimizers for free-discontinuity problems with p(·)-growth

Abstract. A regularity result for free-discontinuity energies defined on the space SBV p(·) of special functions of bounded variation with variable exponent is proved, under the assumption of a log-Ho¨lder continuity for the variable exponent p(x). Our analysis expand on the regularity theory for minimizers of a class of free-discontinuity problems in the nonstandard growth case. This may be seen as a follow-up of the paper [24], dealing with a constant exponent.

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来源期刊

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

自引率

7.10%

发文量

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.