TY - JOUR
T1 - Magnetic Schrödinger operators with delta-type potentials
AU - Rabinovich, Vladimir
N1 - Publisher Copyright:
© 2020 John Wiley & Sons, Ltd.
PY - 2021/8
Y1 - 2021/8
N2 - We consider the magnetic anisotropic Schrödinger operator on (Formula presented.) 1 (Formula presented.) where (Formula presented.) is the vector potential of the magnetic field and W(x) is the scalar potential of the electric field. We assume that aj and ϱij are real-valued functions belonging to the space (Formula presented.) of bounded with first derivatives on (Formula presented.) functions, whereas (Formula presented.) is a complex-valued electric potential. Let Σ be a C2-hypersurface in (Formula presented.) dividing (Formula presented.) on two open domains Ω± with common boundary Σ. We assume that Σ is a closed C2-hypersurface or unbounded hypersurface of bounded geometry. We consider the magnetic Schrödinger operator (Formula presented.) with singular potentials Ws with supports on Σ. We associate with (Formula presented.) an unbounded operator (Formula presented.) in (Formula presented.) generated by Hϱ,a, W with domain in H2(Ω+) ⊕ H2(Ω−) consisting of functions satisfying interaction conditions on Σ. We study the self-adjointness of the operator (Formula presented.) and its Fredholm properties. Moreover, we consider the spectral problem 2 (Formula presented.) and reduce this problem to a spectral problem for some boundary pseudodifferential operators on Σ. We describe the domains in (Formula presented.) where problem (2) has the discrete spectrum.
AB - We consider the magnetic anisotropic Schrödinger operator on (Formula presented.) 1 (Formula presented.) where (Formula presented.) is the vector potential of the magnetic field and W(x) is the scalar potential of the electric field. We assume that aj and ϱij are real-valued functions belonging to the space (Formula presented.) of bounded with first derivatives on (Formula presented.) functions, whereas (Formula presented.) is a complex-valued electric potential. Let Σ be a C2-hypersurface in (Formula presented.) dividing (Formula presented.) on two open domains Ω± with common boundary Σ. We assume that Σ is a closed C2-hypersurface or unbounded hypersurface of bounded geometry. We consider the magnetic Schrödinger operator (Formula presented.) with singular potentials Ws with supports on Σ. We associate with (Formula presented.) an unbounded operator (Formula presented.) in (Formula presented.) generated by Hϱ,a, W with domain in H2(Ω+) ⊕ H2(Ω−) consisting of functions satisfying interaction conditions on Σ. We study the self-adjointness of the operator (Formula presented.) and its Fredholm properties. Moreover, we consider the spectral problem 2 (Formula presented.) and reduce this problem to a spectral problem for some boundary pseudodifferential operators on Σ. We describe the domains in (Formula presented.) where problem (2) has the discrete spectrum.
UR - http://www.scopus.com/inward/record.url?scp=85096704228&partnerID=8YFLogxK
U2 - 10.1002/mma.6992
DO - 10.1002/mma.6992
M3 - Artículo
AN - SCOPUS:85096704228
SN - 0170-4214
VL - 44
SP - 9746
EP - 9764
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 12
ER -