Green’s function for second order elliptic equations with singular lower order coefficients

Seick Kim, Georgios Sakellaris

Research output: Contribution to journalArticle

Abstract

We construct Green’s function for second order elliptic operators of the form (Formula presented.) in a domain and obtain pointwise bounds, as well as Lorentz space bounds. We assume that the matrix of principal coefficients (Formula presented.) is uniformly elliptic and bounded and the lower order coefficients b, c, and d belong to certain Lebesgue classes and satisfy the condition (Formula presented.). In particular, we allow the lower order coefficients to be singular. We also obtain the global pointwise bounds for the gradient of Green’s function in the case when the mean oscillations of the coefficients (Formula presented.) and b satisfy the Dini conditions and the domain is (Formula presented.).

Original languageEnglish
Pages (from-to)228-270
Number of pages43
JournalCommunications in Partial Differential Equations
Volume44
Issue number3
DOIs
Publication statusPublished - 2019 Mar 4

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Second Order Elliptic Equations
Green's function
Coefficient
Mathematical operators
Lorentz Spaces
Henri Léon Lebésgue
Elliptic Operator
Oscillation
Gradient

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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Green’s function for second order elliptic equations with singular lower order coefficients. / Kim, Seick; Sakellaris, Georgios.

In: Communications in Partial Differential Equations, Vol. 44, No. 3, 04.03.2019, p. 228-270.

Research output: Contribution to journalArticle

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