On the regularity theory for quasilinear elliptic systems with the application of Leray-Schauder method

	On the regularity theory for quasilinear elliptic systems with the application of Leray-Schauder method
Journal of Mathematical Modeling
مقاله 23، دوره 13، شماره 1، خرداد 2025، صفحه 169-182 اصل مقاله (187.71 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2024.27119.2387
نویسنده
Mykola Yaremenko^*
The National Technical University of Ukraine, Igor Sikorsky Kyiv Polytechnic Institute, 37, Prospect Beresteiskyi (former Peremohy), Kyiv, Ukraine, 03056
چکیده
In this article, we consider an elliptic system of partial differential equations in the general form \[\sum _{i=1,..., n}\frac{d}{dx_{i} } A_{i} \left(x,\; \overrightarrow{u},\; \nabla \overrightarrow{u}\right) +B\left(x,\; \overrightarrow{u},\; \nabla \overrightarrow{u}\right)=0\] under fair general conditions on its structural coefficients. We study the regularity properties of the solutions to this system, and we establish the existence of a Holder solution by the modified Leray-Schauder fixed-point method and the application of the apriori estimations obtained with utilization of form-boundary conditions.
کلیدواژه‌ها
Quasilinear Partial Differential Equation؛ Holder solution؛ regularity theory؛ Leray-Schauder theorem؛ form-bounded

آمار تعداد مشاهده مقاله: 61 تعداد دریافت فایل اصل مقاله: 116

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