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Keywords:
degenerate elliptic equation; singular gradient lower order term; existence and regularity; Harnack inequality; $L^{m}$-data
degenerate elliptic equation; singular gradient lower order term; existence and regularity; Harnack inequality; $L^{m}$-data
Summary:
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 $1<m<{d}/{p^{-}}$. 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.
References:
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