We study the ∂ ¯ -equation subject to various boundary value conditions on bounded simply connected Lipschitz domains D ⊂ C : for the Dirichlet problem with datum in L p ( b D , σ ) , this is simply a restatement of the fact that members of the holomorphic Hardy spaces are uniquely and completely determined by their boundary values. Here we identify the maximal data spaces and obtain estimates in the optimal p -range for the Dirichlet, Regularity-for-Dirichlet, Neumann, and Robin boundary conditions for ∂ ¯ .
Gryc, W., Lanzani, L., Xiong, J., Zhang, Y. (2026). Boundary value problems for holomorphic functions on Lipschitz planar domains. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 555(2), 1-22 [10.1016/j.jmaa.2025.130135].
Boundary value problems for holomorphic functions on Lipschitz planar domains
Lanzani L.
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2026
Abstract
We study the ∂ ¯ -equation subject to various boundary value conditions on bounded simply connected Lipschitz domains D ⊂ C : for the Dirichlet problem with datum in L p ( b D , σ ) , this is simply a restatement of the fact that members of the holomorphic Hardy spaces are uniquely and completely determined by their boundary values. Here we identify the maximal data spaces and obtain estimates in the optimal p -range for the Dirichlet, Regularity-for-Dirichlet, Neumann, and Robin boundary conditions for ∂ ¯ .| File | Dimensione | Formato | |
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Gryc Lanzani Xiong Zhang 2026 Accepted.pdf
embargo fino al 13/10/2026
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Postprint / Author's Accepted Manuscript (AAM) - versione accettata per la pubblicazione dopo la peer-review
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