On Sharp Hölder Estimates of the Cauchy-Riemann Equation on Pseudoconvex Domains in Cn with One Degenerate Eigenvalue
Let Ω be a smoothly bounded pseudoconvex domain in Cn with one degenerate eigenvalue and assume that there is a smooth holomorphic curve V whose order of contact with bΩ at z0∈bΩ is larger than or equal to η. We show that the maximal gain in Hölder regularity for solutions of the ∂¯-equation is at m...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/731068 |
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| _version_ | 1832567621126455296 |
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| author | Sanghyun Cho Young Hwan You |
| author_facet | Sanghyun Cho Young Hwan You |
| author_sort | Sanghyun Cho |
| collection | DOAJ |
| description | Let Ω be a smoothly bounded pseudoconvex domain in Cn with one degenerate eigenvalue and assume that there is a smooth holomorphic curve V whose order of contact with bΩ at z0∈bΩ is larger than or equal to η. We show that the maximal gain in Hölder regularity for solutions of the ∂¯-equation is at most 1/η. |
| format | Article |
| id | doaj-art-d1864770329d4dbd989747747dd4bf72 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d1864770329d4dbd989747747dd4bf722025-02-03T01:01:06ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/731068731068On Sharp Hölder Estimates of the Cauchy-Riemann Equation on Pseudoconvex Domains in Cn with One Degenerate EigenvalueSanghyun Cho0Young Hwan You1Department of Mathematics, Sogang University, Seoul 121-742, Republic of KoreaDepartment of Mathematics, Indiana University East, Richmond, IN 47374, USALet Ω be a smoothly bounded pseudoconvex domain in Cn with one degenerate eigenvalue and assume that there is a smooth holomorphic curve V whose order of contact with bΩ at z0∈bΩ is larger than or equal to η. We show that the maximal gain in Hölder regularity for solutions of the ∂¯-equation is at most 1/η.http://dx.doi.org/10.1155/2015/731068 |
| spellingShingle | Sanghyun Cho Young Hwan You On Sharp Hölder Estimates of the Cauchy-Riemann Equation on Pseudoconvex Domains in Cn with One Degenerate Eigenvalue Abstract and Applied Analysis |
| title | On Sharp Hölder Estimates of the Cauchy-Riemann Equation on Pseudoconvex Domains in Cn with One Degenerate Eigenvalue |
| title_full | On Sharp Hölder Estimates of the Cauchy-Riemann Equation on Pseudoconvex Domains in Cn with One Degenerate Eigenvalue |
| title_fullStr | On Sharp Hölder Estimates of the Cauchy-Riemann Equation on Pseudoconvex Domains in Cn with One Degenerate Eigenvalue |
| title_full_unstemmed | On Sharp Hölder Estimates of the Cauchy-Riemann Equation on Pseudoconvex Domains in Cn with One Degenerate Eigenvalue |
| title_short | On Sharp Hölder Estimates of the Cauchy-Riemann Equation on Pseudoconvex Domains in Cn with One Degenerate Eigenvalue |
| title_sort | on sharp holder estimates of the cauchy riemann equation on pseudoconvex domains in cn with one degenerate eigenvalue |
| url | http://dx.doi.org/10.1155/2015/731068 |
| work_keys_str_mv | AT sanghyuncho onsharpholderestimatesofthecauchyriemannequationonpseudoconvexdomainsincnwithonedegenerateeigenvalue AT younghwanyou onsharpholderestimatesofthecauchyriemannequationonpseudoconvexdomainsincnwithonedegenerateeigenvalue |