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

Document Type : Research Article

Author

The National Technical University of Ukraine, Igor Sikorsky Kyiv Polytechnic Institute, 37, Prospect Beresteiskyi (former Peremohy), Kyiv, Ukraine, 03056

Abstract

 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.

Keywords

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References

 
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Journal of Mathematical Modeling
Volume 13, Issue 1
March 2025
Pages 169-182

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