Submitted:
15 September 2026
Posted:
16 September 2026
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Abstract
This paper studies a quasilinear and nonuniformly coercive elliptic Neumann problem with both right hand sides in \(L^1(\Omega)\) (PDE) and boundary data in \(L^1(\partial\Omega)\), in the context of Sobolev spaces with variable exponent. We analyze the existence and the uniqueness of renormalized solutions to this problem.
Keywords:
variable exponent Sobolev spaces
; Neumann boundary condition
; renormalized solutions
; uniqueness
; quasilinear elliptic problem
; nonuniformly coercive operator
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