Document Type

Article

Publication Date

1-1-2023

Abstract

We prove the uniqueness property for a class of entire solutions to the equation (Formula presented) where σ is a nonnegative locally finite measure in Rn, absolutely continuous with respect to the p-capacity, and div A(x, ∇u) is the A-Laplace operator, under standard growth and monotonicity assumptions of order p (1 < p < ∞) on A(x, ξ) (x, ξ ∈ Rn); the model case A(x, ξ) = ξ|ξ|p−2 corresponds to the p-Laplace operator ∆p on Rn. Our main results establish uniqueness of solutions to a similar problem,(Formula presented) in the sub-natural growth case 0 < q < p − 1, where µ, σ are nonnegative locally finite measures in Rn, absolutely continuous with respect to the p-capacity, and A(x, ξ) satisfies an additional homogeneity condition, which holds in particular for the p-Laplace operator.

Publication Source (Journal or Book title)

Mathematics in Engineering

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