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April 16, 2026Filomat0 citationsOpen Access

Renormalized solutions for some nonlinear degenerated elliptic problems in weighted Sobolev space with variable exponents

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MFMohammed El FatryMMMounir MekkourYAYoussef Akdim

Key Points

  • The aim is to demonstrate the existence of a renormalized solution for a specific nonlinear elliptic equation.
  • Proved the existence of solutions to the nonlinear elliptic equation
  • Analyzed the equation within the context of weighted Sobolev spaces
  • Considered cases where the solution blows up for finite values
  • Established existence of a renormalized solution under given conditions
  • Characterized the nature of the solutions in terms of boundary behavior
  • Showed the implications for a category of elliptic equations with specific properties

Abstract

In this article, we prove the existence of a renormalised solution to the problem of the nonlinear elliptic equation: cases -div (a (x, u, Du) ) = f in, \\ u = 0 on, cases, (1) where a (x, u, Du) is blow-up for a finite value m of the unknown u and the data f L¹ ().

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Cite This Study

Fatry et al. (2025) studied this question.

synapsesocial.com/papers/69e07e3b2f7e8953b7cbf49ahttps://doi.org/10.2298/fil2526101e
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