Regularity of solutions to the polyharmonic equation in general domains

Svitlana Mayboroda; Vladimir Maz'ya

doi:10.1007/s00222-013-0464-1

Regularity of solutions to the polyharmonic equation in general domains

Svitlana Mayboroda
, Vladimir Maz'ya

School of Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

The present paper establishes boundedness of [m - n/2 + 1/2] derivatives for the solutions to the polyharmonic equation of order 2m in arbitrary bounded open sets of ℝⁿ, 2 ≤ n ≤ 2m + 1, without any restrictions on the geometry of the underlying domain. It is shown that this result is sharp and cannot be improved in general domains. Moreover, it is accompanied by sharp estimates on the polyharmonic Green function.

Original language	English (US)
Pages (from-to)	1-68
Number of pages	68
Journal	Inventiones Mathematicae
Volume	196
Issue number	1
DOIs	https://doi.org/10.1007/s00222-013-0464-1
State	Published - Apr 2014

Publisher link

10.1007/s00222-013-0464-1

Find It

Find It at U of M Libraries

Cite this

@article{34cd1dee4a194734b93666130b78a236,

title = "Regularity of solutions to the polyharmonic equation in general domains",

abstract = "The present paper establishes boundedness of [m - n/2 + 1/2] derivatives for the solutions to the polyharmonic equation of order 2m in arbitrary bounded open sets of ℝn, 2 ≤ n ≤ 2m + 1, without any restrictions on the geometry of the underlying domain. It is shown that this result is sharp and cannot be improved in general domains. Moreover, it is accompanied by sharp estimates on the polyharmonic Green function.",

author = "Svitlana Mayboroda and Vladimir Maz'ya",

year = "2014",

month = apr,

doi = "10.1007/s00222-013-0464-1",

language = "English (US)",

volume = "196",

pages = "1--68",

journal = "Inventiones Mathematicae",

issn = "0020-9910",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Regularity of solutions to the polyharmonic equation in general domains

AU - Mayboroda, Svitlana

AU - Maz'ya, Vladimir

PY - 2014/4

Y1 - 2014/4

N2 - The present paper establishes boundedness of [m - n/2 + 1/2] derivatives for the solutions to the polyharmonic equation of order 2m in arbitrary bounded open sets of ℝn, 2 ≤ n ≤ 2m + 1, without any restrictions on the geometry of the underlying domain. It is shown that this result is sharp and cannot be improved in general domains. Moreover, it is accompanied by sharp estimates on the polyharmonic Green function.

AB - The present paper establishes boundedness of [m - n/2 + 1/2] derivatives for the solutions to the polyharmonic equation of order 2m in arbitrary bounded open sets of ℝn, 2 ≤ n ≤ 2m + 1, without any restrictions on the geometry of the underlying domain. It is shown that this result is sharp and cannot be improved in general domains. Moreover, it is accompanied by sharp estimates on the polyharmonic Green function.

UR - https://www.scopus.com/pages/publications/84896399632

UR - https://www.scopus.com/pages/publications/84896399632#tab=citedBy

U2 - 10.1007/s00222-013-0464-1

DO - 10.1007/s00222-013-0464-1

M3 - Article

AN - SCOPUS:84896399632

SN - 0020-9910

VL - 196

SP - 1

EP - 68

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

IS - 1

ER -

Regularity of solutions to the polyharmonic equation in general domains

Abstract

Publisher link

Find It

Other files and links

Fingerprint

Cite this