TY - JOUR
T1 - Asymptotic behavior of solutions to elliptic and parabolic equations with unbounded coefficients of the second order in unbounded domains
AU - Kozono, Hideo
AU - Terasawa, Yutaka
AU - Wakasugi, Yuta
N1 - Funding Information:
This work was supported by JSPS Grant-in-Aid for Scientific Research(S) Grant Number JP16H06339.
PY - 2020
Y1 - 2020
N2 - We study an asymptotic behavior of solutions to elliptic equations of the second order in a two dimensional exterior domain. Under the assumption that the solution belongs to Lq with q∈ [2 , ∞) , we prove a pointwise asymptotic estimate of the solution at the spatial infinity in terms of the behavior of the coefficients. As a corollary, we obtain the Liouville-type theorem in the case when the coefficients may grow at the spacial infinity. We also study a corresponding parabolic problem in the n-dimensional whole space and discuss the energy identity for solutions in Lq. As a corollary we show also the Liouville-type theorem for both forward and ancient solutions.
AB - We study an asymptotic behavior of solutions to elliptic equations of the second order in a two dimensional exterior domain. Under the assumption that the solution belongs to Lq with q∈ [2 , ∞) , we prove a pointwise asymptotic estimate of the solution at the spatial infinity in terms of the behavior of the coefficients. As a corollary, we obtain the Liouville-type theorem in the case when the coefficients may grow at the spacial infinity. We also study a corresponding parabolic problem in the n-dimensional whole space and discuss the energy identity for solutions in Lq. As a corollary we show also the Liouville-type theorem for both forward and ancient solutions.
KW - Asymptotic behavior
KW - Elliptic and parabolic equations of second order
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U2 - 10.1007/s00208-020-02032-2
DO - 10.1007/s00208-020-02032-2
M3 - Article
AN - SCOPUS:85087303201
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
ER -