Linear differential systems with measurable coefficients

Elliptic Differential Equations with Measurable Coefficients

We prove the unique solvability of second order elliptic equations in non-divergence 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.

On systems of linear fractional differential equations with constant coefficients

This paper deals with the study of linear systems of fractional differential equations such as the following system: 0096-3 doi:10 * Co E-m Y ða 1⁄4 AðxÞY þ BðxÞ; ð1Þ where Y ða is the Riemann–Liouville or the Caputo fractional derivative of order a (0 < a 5 1), and AðxÞ 1⁄4 a11ðxÞ a1nðxÞ . . . . . . . . . an1ðxÞ annðxÞ 0BBBBBB@ 1CCCCCCA; BðxÞ 1⁄4 b1ðxÞ . . . . . . . . . bnðxÞ 0BBBBBB@ 1CCCCCCA...

Higher-Order Linear Differential Systems with Truncated Coefficients

We consider the following problem: given a linear differential system with formal Laurent series coefficients, we want to decide whether the system has non-zero Laurent series solutions, and find all such solutions if they exist. Let us also assume we need only a given positive integer number l of initial terms of these series solutions. How many initial terms of the coefficients of the origina...

Linear Differential Systems with Infinite Power Series Coefficients (Invited Talk)

Parabolic Equations with Measurable Coefficients

We investigate the unique solvability of second order parabolic equations in non-divergence form in W 1,2 p ((0, T ) × R), p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables.