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.
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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 -