Regular Oblique Derivative Problems in Sobolev Spaces

Kazuaki Taira ()
Additional contact information
Kazuaki Taira: University of Tsukuba, The College of Mathematics

Chapter Chapter 16 in Real Analysis Methods for Markov Processes, 2024, pp 501-510 from Springer

Abstract: Abstract ThisRegular oblique derivative problem chapterOblique derivative problem isElliptic differential operator devoted to the study of the regular oblique derivative problem for a second order, uniformly elliptic differential operator withSecond order elliptic differential operator discontinuous coefficients in the framework of $$L^{p}$$ L p Sobolev spaces. More precisely, we consider a second order, uniformly elliptic differential operator withVMO (vanishing mean oscillation)@VMO vanishing mean oscillation (VMO) coefficientsVanishing mean oscillation (VMO) and an oblique derivative boundary operator that is nowhere tangential to the boundary. We state global regularizing property of the oblique derivative problem in the framework of $$L^{p}$$ L p Sobolev spaces (Theorem 16.1). Furthermore, we state an existence and uniqueness theorem for the oblique derivative problem in the framework of $$L^{p}$$ L p Sobolev spaces (Theorem 16.2).

Date: 2024
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-97-3659-1_16

Ordering information: This item can be ordered from
http://www.springer.com/9789819736591

DOI: 10.1007/978-981-97-3659-1_16

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().