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This is a Quantitative Study study.

September 22, 2025Open Access

Pathwise regularity of solutions for a class of elliptic SPDEs with symmetric Lévy noise

Key Points

A unique random-field solution exists for elliptic SPDEs driven by symmetric Lévy noise, ensuring continuity.
Under certain conditions, the mild solution's existence is shown using the Green's function methodology.
The analysis encompasses the spectral fractional Laplacian, validating the findings for power γ greater than d/2.
Dirichlet boundary conditions ensure that solutions vanish on the boundary of the defined domain.

Abstract

In this article, we investigate the existence and uniqueness of random-field solutions to the elliptic SPDE -Lu=ξ on a bounded domain D with Dirichlet boundary conditions u=0 on D, driven by symmetric Lévy noise ξ. Under general sufficient conditions on the coefficients of the second-order operator L, we prove the existence of a mild solution via the corresponding Green's function and show that the same framework applies to the spectral fractional Laplacian of power γ (0, ). In particular, whenever γ>d2, the solution admits a continuous modification.

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Cite This Study

Juan José de la Vega Jiménez (Wed,) studied this question.

synapsesocial.com/papers/68d46fdc31b076d99fa6a6b8 https://doi.org/https://doi.org/10.48550/arxiv.2507.12656

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