We study the Poincaré problem for linear uniformly parabolic operator P with discontinuous coefficients. The boundary operator is defined in terms of oblique derivative with respect to a vector field l which points outward the domain or becomes tangential to the boundary on a set of possibly positive measure. A’priori estimates and unique strong solvability are obtained in W^(2,1)_p(Q) for all p\in (1,\infty).
W^{2,1}_p-solvability for the parabolic Poincarè problem,
SOFTOVA PALACHEVA, Lyoubomira
2004-01-01
Abstract
We study the Poincaré problem for linear uniformly parabolic operator P with discontinuous coefficients. The boundary operator is defined in terms of oblique derivative with respect to a vector field l which points outward the domain or becomes tangential to the boundary on a set of possibly positive measure. A’priori estimates and unique strong solvability are obtained in W^(2,1)_p(Q) for all p\in (1,\infty).File in questo prodotto:
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