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Existence of Dirichlet and Neumann Traces for Higher-Order Elliptic Solutions

Trace theorems showing that a solution of a 2m-order elliptic equation with t-independent coefficients in the half-space has Dirichlet and Neumann boundary values in Lebesgue or homogeneous Sobolev spaces whenever a Lusin area-integral norm of its m-th gradient is finite — the converse direction to well-posedness.

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Dirichlet and Neumann boundary values of solutions to higher order elliptic equations

Barton, Hofmann and Mayboroda (March 2017 preprint, math.AP, 41 pages) prove trace theorems for solutions of linear elliptic differential equations of order 2m, at least 2, in the upper half-space. T…