Local behaviour of the second order derivatives of solutions to p-Laplace equations

Q: What type of study is this?

This is a Quantitative Study study.

Felice Iandoli; Domenico Vuono

doi:10.1007/s00526-025-03174-4

October 18, 2025Calculus of Variations and Partial Differential EquationsOpen Access

Local behaviour of the second order derivatives of solutions to p-Laplace equations

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Key Points

Estimates show the behaviour of second derivatives as p approaches 2 in a p-laplace equation.
L-infinity type estimates highlight how these derivatives behave near specific points in the domain.
The p-laplace operator facilitates understanding intricate local behaviours in solutions to differential equations.
This analysis could influence further understanding and applications in non-linear analysis and partial differential equations.

Implication

Analysis provides L-infinity estimates for second derivatives as p approaches 2, revealing local behaviour.

Abstract

We consider the equation - Δ ₚ u = f(x) - Δ p u = f ( x ) in Ω , Ω , where Δ ₚ Δ p is the p -Laplace operator. We provide L∞ L ∞ -type estimates for the second derivatives of solutions when p approaches to 2.

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Cite This Study

Iandoli et al. (2025) studied this question.

synapsesocial.com/papers/68f4b10d3d9d770bbc6970e6 https://doi.org/10.1007/s00526-025-03174-4

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Local behaviour of the second order derivatives of solutions to p-Laplace equations

Key Points

Implication

Abstract

Discussion

Cite This Study

Local behaviour of the second order derivatives of solutions to p-Laplace equations

Key Points

Implication

Abstract

Discussion

Cite This Study

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