The Behaviour of Solutions the Mixed Boundary Problem to Nonlinear Elliptic Equations in Orlicz-Morrey Spaces

We obtained estimates in generalized Orlicz-Morrey spaces are used to study global regularity of the solution of the mixed boundary problem of nonlinear elliptic equations in divergence form over a bounded non-smooth domain. For these is we used of Calderon-Zygmund theory. The exploration of nonlinear reactions, drift, and diffusion processes has garnered significant attention, serving as mathematical models for various applied problems. One such example involves the diffusion processes of electrically charged species during phase transitions and transport in porous media. Additionally, it is worth mentioning that in semiconductor theory, weight functions possess derivatives. Another illustrative instance arises in the context of phase separation problems, where the commonly employed tools include Fermi integrals and Fermi functions. This problems is connected with of nonlinear process which arise as mathematical models of different applied problems. The qualitative property of solution is investigated. The theorems obtained in this article have important applied significance in various issues of mechanics, physics, biology and other applied fields. Also at the end of the article there are specific results where the results obtained in the article are applied. Also at the end of the article there are specific results where the results obtained in the article are applied.