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SUMMARY:Georgios Sakellaris (Autonomous University of Barcelona)
DTSTART:20200611T150000Z
DTEND:20200611T155000Z
DTSTAMP:20260423T010013Z
UID:anpdews/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/anpdews/29/"
 >Green's function for second order elliptic equations with  singular lower
  order coefficients and applications</a>\nby Georgios Sakellaris (Autonomo
 us University of Barcelona) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nW
 e will discuss Green's function for second order elliptic \noperators of t
 he form $\\mathcal{L}u=-\\text{div}(A\\nabla u+bu)+c\\nabla \nu+du$ in dom
 ains $\\Omega\\subseteq\\mathbb R^n$\, for $n\\geq 3$. We will \nassume th
 at $A$ is elliptic and bounded\, and also that \n$d\\geq\\text{div}b$ or $
 d\\geq\\text{div}c$ in the sense of distributions.\n\nIn the setting of Lo
 rentz spaces\, we will explain why the assumption \n$b-c\\in L^{n\,1}(\\Om
 ega)$ is optimal in order to obtain a pointwise \nbound of the form $G(x\,
 y)\\leq C|x-y|^{2-n}$. Under the assumption \n$d\\geq\\text{div}b$\, we wi
 ll also discuss why this assumption is \nnecessary to even have weak type 
 bounds on Green's function. Finally\, \nfor the case $d\\geq\\text{div}c$\
 , we will deduce a maximum principle \nand a Moser type estimate\, showing
  again that the assumption $b-c\\in \nL^{n\,1}(\\Omega)$ is optimal.\n\nOu
 r estimates will be scale invariant and no regularity on \n$\\partial\\Ome
 ga$ will be imposed. In addition\, $\\mathcal{L}$ will not \nbe assumed to
  be coercive\, and there will be no smallness assumption \non the lower or
 der coefficients.\n
LOCATION:https://researchseminars.org/talk/anpdews/29/
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