Green's function for second order parabolic equations with singular lower order coefficients
| Autor: | Longjuan Xu, Seick Kim |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Connected space Applied Mathematics Mathematics::Analysis of PDEs Order (ring theory) General Medicine Physics::Classical Physics Parabolic partial differential equation Omega Combinatorics symbols.namesake Mathematics - Analysis of PDEs Green's function Bounded function Physics::Space Physics symbols FOS: Mathematics Nabla symbol Lp space Analysis Analysis of PDEs (math.AP) |
| Popis: | We construct Green's functions for second order parabolic operators of the form $Pu=\partial_t u-{\rm div}({\bf A} \nabla u+ \boldsymbol{b}u)+ \boldsymbol{c} \cdot \nabla u+du$ in $(-\infty, \infty) \times \Omega$, where $\Omega$ is an open connected set in $\mathbb{R}^n$. It is not necessary that $\Omega$ to be bounded and $\Omega = \mathbb{R}^n$ is not excluded. We assume that the leading coefficients $\bf A$ are bounded and measurable and the lower order coefficients $\boldsymbol{b}$, $\boldsymbol{c}$, and $d$ belong to critical mixed norm Lebesgue spaces and satisfy the conditions $d-{\rm div} \boldsymbol{b} \ge 0$ and ${\rm div}(\boldsymbol{b}-\boldsymbol{c}) \ge 0$. We show that the Green's function has the Gaussian bound in the entire $(-\infty, \infty) \times \Omega$. Comment: 20 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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