A Liouville-type theorem for elliptic equations with singular coefficients in bounded domains

被引：0

作者：

Stefano Biagi

Fabio Punzo

机构：

[1] Politecnico di Milano,Dipartimento di Matematica

来源：

Calculus of Variations and Partial Differential Equations | 2023年 / 62卷

关键词：

35A02; 35B53; 35J15;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We investigate Liouville-type theorems for elliptic equations with a drift and with a potential posed in bounded domains. We provide sufficient conditions on the potential and on the drift term in order to the equation does not admit nontrivial bounded solutions. We also show that such conditions are optimal. Indeed, when they fail, the elliptic equation possesses infinitely many bounded solutions.

引用

共 10 条

[1]

Fichera G(1956)Sulle equazioni differenziali lineari ellittico-paraboliche del secondo ordine Mem. Accad. Naz. Lincei I 1-30

[2]

Grigor’yan A(1990)Bounded solution for the Schrödinger equation on noncompact Riemannian manifolds J. Soviet Math. 51 2340-2349

[3]

Grigor’yan A(1999)Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds Bull. Am. Math. Soc. 36 135-249

[4]

Khasminskii RZ(1958)Diffusion processes and elliptic differential equations degenerating at the boundary of the domain Theory Prob. Appl. 4 400-419

[5]

Pozio MA(2008)Criteria for well-posedness of degenerate elliptic and parabolic problems J. Math. Pures Appl. 90 353-386

[6]

Punzo F(2009)Uniqueness of solutions to degenerate elliptic problems with unbounded coefficients Ann. Inst. H. Poincaré Anal. Non Lin. 26 2001-2024

[7]

Tesei A(1939)On the volumes of Tubes Am. J. Math. 61 461-472

[8]

Punzo F(undefined)undefined undefined undefined undefined-undefined

[9]

Tesei A(undefined)undefined undefined undefined undefined-undefined

[10]

Weyl H(undefined)undefined undefined undefined undefined-undefined

← 1 →