Josh Kline

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20242026

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math.AP2025

Well-posedness of Dirichlet boundary value problems for reflected fractional $p$ -Laplace-type inhomogeneous equations in compact doubling metric measure spaces

Josh Kline, Feng Li, Nageswari Shanmugalingam

In this paper we consider the setting of a locally compact, non-complete metric measure space $(Z, d, I^½)$ equipped with a doubling measure $I^½$ , under the condition that the boundar…

math.AP2025

Regularity of sets of finite fractional perimeter and nonlocal minimal surfaces in metric measure spaces

Josh Kline

In the setting of a doubling metric measure space, we study regularity of sets with finite $s$ -perimeter, that is, sets whose characteristic functions have finite Besov energy, wit…

math.AP2024

Self-improvement of fractional Hardy inequalities in metric measure spaces via hyperbolic fillings

Sylvester Eriksson-Bique, Josh Kline

In this paper, we prove a self-improvement result for $(I^¸, p)$ -fractional Hardy inequalities, in both the exponent $1 < p < \infty$ and the regularity parameter $0 < I^¸ < 1$ , for bounded d…

Well-posedness of Dirichlet boundary value problems for reflected fractional p-Laplace-type inhomogeneous equations in compact doubling metric measure spaces

Regularity of sets of finite fractional perimeter and nonlocal minimal surfaces in metric measure spaces

Self-improvement of fractional Hardy inequalities in metric measure spaces via hyperbolic fillings

Well-posedness of Dirichlet boundary value problems for reflected fractional $p$ -Laplace-type inhomogeneous equations in compact doubling metric measure spaces