This paper is a continuation of recent work by Guo-Xiang-Zheng[10]. We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation $\begin{equation*} \Delta^{2}u=\Delta(V\nabla u)+{\rm div}(w\nabla u)+(\nabla\omega+F)\cdot\nabla u+f\qquad\text{in }B^{4},\end{equation*}$ under the smallest regularity assumptions of $V,w,\omega, F$, where $f$ belongs to some Morrey spaces. This work was motivated by many geometrical problems such as the flow of biharmonic mappings. Our results deepens the $L^p$ type regularity theory of [10], and generalizes the work of Du, Kang and Wang [4] on a second order problem to our fourth order problems.
Changlin XIANG
,
Gaofeng ZHENG
. SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION[J]. Acta mathematica scientia, Series B, 2024
, 44(2)
: 420
-430
.
DOI: 10.1007/s10473-024-0202-3
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