Publication details
Boundary value problems for semilinear Schrödinger equations with singular potentials and measure data
| Authors | |
|---|---|
| Year of publication | 2024 |
| Type | Article in Periodical |
| Magazine / Source | Mathematische Annalen |
| MU Faculty or unit | |
| Citation | |
| Web | https://link.springer.com/article/10.1007/s00208-023-02764-x |
| Doi | http://dx.doi.org/10.1007/s00208-023-02764-x |
| Keywords | Semilinear elliptic equations; Singular elliptic equations; Schrödinger operator; Schrödinger equation |
| Description | We study boundary value problems with measure data in smooth bounded domains Omega, for semilinear equations. Specifically we consider problems of the form - L(V)u + f (u) = tau in Omega and tr(V)u = nu on partial derivative Omega, where L-V = Delta + V, f. is an element of C(R) is monotone increasingwith f (0) = 0 and tr V u denotes themeasure boundary trace of u associated with L-V. The potential V is an element of C-1(Omega) typically blows up at a set F subset of partial derivative Omega as dist (x, F)(-2). In general the above boundary value problem may not have a solution. We are interested in questions related to the concept of 'reduced measures', introduced in Brezis et al. (Ann Math Stud 163:55-109, 20072007) for V = 0. Our results extend results of [4] and Brezis and Ponce (J Funct Anal 229(1):95-120, 2005) and apply to a larger class of nonlinear terms f. In the case of signed measures, some of the present results are new even for V = 0. |
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