Abstract
We give a direct and elementary proof for the trace theorem in L p -based Sobolev spaces, when the domain is the unit disk. We also consider the Dirichlet boundary problem for the Laplace equation, where the boundary value is a function in the Besov space. The Poisson kernel enables us to solve this problem in the unit disk more easily than in a general domain.
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Miyazaki, Y. Sobolev Trace Theorem and the Dirichlet Problem in the Unit Disk. Milan J. Math. 82, 297–312 (2014). https://doi.org/10.1007/s00032-014-0222-x
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DOI: https://doi.org/10.1007/s00032-014-0222-x