김도윤 교수

We prove the unique solvability of second order elliptic equations in nondivergence form in Sobolev spaces. The coefficients of the second order terms are measurable in one variable and VMO in other variables. From this result, we obtain the weak uniqueness of the Martingale problem associated with the elliptic equations.

We consider second order parabolic and elliptic systems with leading coefficients having the property of vanishing mean oscillation (VMO) in the spatial variables. An Lq -Lp theory is established for systems both in divergence and non-divergence form.

The unique solvability results for second order parabolic and elliptic equations in Sobolev spaces with mixed norms are presented. The second order coefficients are measurable in one spatial variable and VMO (vanishing mean oscillation) in the other spatial variables. In the parabolic case, the coefficients (except a 11 ) are further allowed to be only measurable in time. We first prove the solvability results for equations in the whole Euclidean space. Then, using these results as well as some

We prove that the well‐known trace theorem for weighted Sobolev spaces holds true under minimal regularity assumptions on the domain. Using this result, we prove the existence of a bounded linear right inverse of the trace operator for Sobolev‐Slobodeckij spaces when s − 1/ p is an integer.