Zusammenfassung für den Vortrag am 11.04.2019 (14:00 Uhr)
Arbeitsgemeinschaft ANGEWANDTE ANALYSISWiktoria Zaton (Universität Bonn)
On the well-posedness for higher order parabolic equations with rough coefficients
In the first part we study the existence and uniqueness of solutions to the higher order parabolic Cauchy problems on the upper half space, given by ∂tu = (−1)m+1divmA(t,x)∇mu and Lp initial data space. The (complex) coefficients are only assumed to be elliptic and bounded measurable. Our approach follows the recent developments in the field for the case m = 1. In the second part we consider the BMO space of initial data. We will see that the Carleson measure condition <center class="math-display"> <img src="/fileadmin/lecture_img/tex_28530c0x.png" alt=" ∫ ∫ ---1--- r m m 2m 2dxdt xsu∈pℝnsru&#x003E;p0 |B (x,r)| B(x,r) 0 |t ∇ u(t ,x)| t &#x003C; ∞ " class="math-display"></center> provides, up to polynomials, a well-posedness class for BMO. In particular, since the operator L is arbitrary, this also leads to a new, broad Carleson measure characterization of BMO in terms of solutions to the parabolic system.