an:06099201
Zbl 1255.35064
Lu, Guozhen; Wang, Peiyong; Zhu, Jiuyi
Liouville-type theorems and decay estimates for solutions to higher order elliptic equations
EN
Ann. Inst. Henri Poincar??, Anal. Non Lin??aire 29, No. 5, 653-665 (2012).
00309133
2012
j
35B53 35J40 35J47 35B45
polyharmonic operators on half spaces; Dirichlet problem; Navier boundary condition; doubling property; without boundedness assumptions; rescaling technique
Summary: Liouville-type theorems are powerful tools in partial differential equations. Boundedness assumptions of solutions are often imposed in deriving such Liouville-type theorems. In this paper, we establish some Liouville-type theorems without the boundedness assumption of nonnegative solutions to certain classes of elliptic equations and systems. Using a rescaling technique and doubling lemma developed recently in [\textit{P. Pol????ik} et al., Duke Math. J. 139, No. 3, 555--579 (2007; Zbl 1146.35038)], we improve several Liouville-type theorems in higher order elliptic equations, some semilinear equations and elliptic systems. More specifically, we remove the boundedness assumption of the solutions which is required in the proofs of the corresponding Liouville-type theorems in the recent literature. Moreover, we also investigate the singularity and decay estimates of higher order elliptic equations.
Zbl 1146.35038