PreprintCC BY 4.0arXiv
On the W2,p solvability for mixed boundary value problems
Abstract
We establish global W2,p solvability for the Poisson equation with mixed Dirichlet--Neumann boundary conditions in two classes of domains in all dimensions n≥ 2. For C1,α domains with a Reifenbeg flat interface, we obtain the optimal range 1<p<4/3, provided that α>1−1/p. For Lipschitz polyhedra with facewise boundary decompositions, we obtain solvability for p close to $1$. In both settings, we establish endpoint W2,1 solvability for data in an adapted atomic Hardy space. Applications of the methods to Lamé systems are also discussed.
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BibTeX
@misc{khandelwal2026solvability,
title = {{On the $W^2,p$ solvability for mixed boundary value problems}},
author = {Rohit Khandelwal and Zongyuan Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30090},
eprint = {2609.30090},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30090},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the W^2,p solvability for mixed boundary value problems
AU - Rohit Khandelwal
AU - Zongyuan Li
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30090
UR - https://arxiv.org/abs/2609.30090
AB - We establish global W^2,p solvability for the Poisson equation with mixed Dirichlet--Neumann boundary conditions in two classes of domains in all dimensions n≥ 2. For C^1,α domains with a Reifenbeg flat interface, we obtain the optimal range 1<p<4/3, provided that α>1−1/p. For Lipschitz polyhedra with facewise boundary decompositions, we obtain solvability for p close to $1$. In both settings, we establish endpoint W^2,1 solvability for data in an adapted atomic Hardy space. Applications of the methods to Lamé systems are also discussed.
ER -