Radjia Teyar, Hichem Khelifi, Fares Mokhtari
Degenerate elliptic equations with variable exponents and multiple types of terms

Abstract: We present a comprehensive analysis of the existence and regularity of distributional solutions for a given class of nonlinear degenerate elliptic equations. The equations under consideration contain singular gradient lower order terms and are related to the L^{m} data, where the exponent m satisfies 1. To deal with this problem, we use a functional framework that includes Lebesgue-Sobolev spaces with variable exponents. Our findings provide valuable additions to the previous research discussed in Nonlinear degenerate p(x)-Laplacian equation with singular gradient and lower order term (2023) by H. Khelifi and M. A. Zouatini.

Keywords: degenerate elliptic equation; singular gradient lower order term; existence and regularity; Harnack inequality; L^{m}-data

DOI: DOI 10.14712/1213-7243.2025.007
AMS Subject Classification: 35J62 35J70 35J75