Boundary value problems with signed measure data for semilinear Schrödinger equations

2023/05/17 by Moshe Marcus, Marcus, Moshe
Computer Science · Mathematics · #35J60 #35J75 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2305.10370

openalex publication_date 2023/05/17 · openalex created_date 2023/05/20 · openalex updated_date 2026/07/28

Abstract

Consider operators L_V:=Δ+ V in a bounded Lipschitz domain Ω⊂ ℝ^N. Assume that V∈ C^α(Ω) satisfies |V(x)| ≤ a dist(x,∂Ω)^-2 in Ω and that L_V has a (minimal) ground state Φ_V in Ω. We derive a representation formula for signed supersolutions (or subsolutions) of L_Vu=0 possessing an L_V boundary trace. We apply this formula to the study of some questions of existence and uniqueness for an associated semilinear boundary value problem with signed measure data.

Related

• Boundary value problems for semilinear Schrödinger equations with singular potentials and measure data
• Schrodinger equations with very singular potentials in Lipschitz domains
• Estimates of sub and super solutions of Schrödinger equations with very singular potentials
• Schrödinger equations with singular potentials: linear and nonlinear boundary value problems
• Semilinear elliptic Schrödinger equations involving singular potentials and source terms