A relationship between the Dirichlet and Regularity Problems for elliptic equations
Shen, Zhongwei
Original · EN
We study the relationship between the solvability of the Lᵖ Dirichlet problem (D)ₚ and that of the Lq regularity problem (R)q for second order elliptic equations with bounded measurable coefficients. It is known that the solvability of (R)ₚ implies that of (D)ₚ′. In this note we show that if (D)ₚ′ is solvable, then either (R)ₚ is solvable or (R)q is not solvable for any 1<q<∞.
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