拟线性偏微分方程，插值空间和Hölderian映射

IF 0.6 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2023-11-15 DOI:10.1007/s10476-023-0245-z

I. Ahmed, A. Fiorenza, M. R. Formica, A. Gogatishvili, A. El Hamidi, J. M. Rakotoson

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引用次数: 0

摘要

在tartar[59]的工作中，我们通过研究映射在k泛函上的作用以及插值空间与对数函数之间的作用，得到了赋范空间之间α-Hölderian映射的非线性插值的一些新结果。我们应用这些结果得到了形式为$$-\text{div}(\widehat{a}(\nabla u))+V(u)=f,$$的拟线性方程解梯度的一些正则性结果，其中V是非线性势，f属于非标准空间，如Lorentz-Zygmund空间。我们展示了几个结果;例如，在适当的α值和适当的V和假设下，映射$\cal{T}:\cal{T}f=\nabla u$是局部的或全局的α-Hölderian。

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Quasilinear PDEs, Interpolation Spaces and Hölderian mappings

As in the work of Tartar [59], we develop here some new results on nonlinear interpolation of α-Hölderian mappings between normed spaces, by studying the action of the mappings on K-functionals and between interpolation spaces with logarithm functions. We apply these results to obtain some regularity results on the gradient of the solutions to quasilinear equations of the form

$$-\text{div}(\widehat{a}(\nabla u))+V(u)=f,$$

where V is a nonlinear potential and f belongs to non-standard spaces like Lorentz–Zygmund spaces. We show several results; for instance, that the mapping $\cal{T}:\cal{T}f=\nabla u$ is locally or globally α-Hölderian under suitable values of α and appropriate hypotheses on V and â.

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来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.