-Solvability for the Parabolic Poincaré Problem
Lubomira G. Softova · Communications in Partial Differential Equations · 2005
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 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 for all p ∈ (1, ∞).