W^{2,1}_p Solvability for Parabolic Poincare Problem
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arXiv
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| Format: | Preprint |
| Publié: |
2003
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| _version_ | 1866914190255456256 |
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| author | Softova, Lubomira G. |
| author_facet | Softova, Lubomira G. |
| contents | We study Poincaré problem for a linear uniformly parabolic operator $¶$ in a cylinder $Q=Ω\times (0,T).$ The boundary operator $\B$ is defined by an oblique derivative with respect to a tangential vector field $ł$ defined on the lateral boundary $S.$ The coefficients of $¶$ are supposed to be $VMO$ away from the set of tangency $E$ and to possess higher regularity in $x$ near to $E.$ A unique strong solvability result is obtained in $W^{2,1}_p(Q)$ for all $p\in (1,\infty).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0307377 |
| institution | arXiv |
| publishDate | 2003 |
| record_format | arxiv |
| spellingShingle | W^{2,1}_p Solvability for Parabolic Poincare Problem Softova, Lubomira G. Analysis of PDEs Functional Analysis 35K20, 35B45 We study Poincaré problem for a linear uniformly parabolic operator $¶$ in a cylinder $Q=Ω\times (0,T).$ The boundary operator $\B$ is defined by an oblique derivative with respect to a tangential vector field $ł$ defined on the lateral boundary $S.$ The coefficients of $¶$ are supposed to be $VMO$ away from the set of tangency $E$ and to possess higher regularity in $x$ near to $E.$ A unique strong solvability result is obtained in $W^{2,1}_p(Q)$ for all $p\in (1,\infty).$ |
| title | W^{2,1}_p Solvability for Parabolic Poincare Problem |
| topic | Analysis of PDEs Functional Analysis 35K20, 35B45 |
| url | https://arxiv.org/abs/math/0307377 |