Abstract
In this paper we present a simpler proof of a Theorem due to M. Aizenman and B. Simon in [1] which states that the Schrödinger equation (1/2)Δu + q u = 0 in Rd, d≥3, q∈Kd, given in distributional sense, has a continuous solution in an open set D in Rd.
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References
Aizenman, M. and Simon, B., Brownian motion and Harnack inequality for Schrödinger Operators, Commun. Pure and Applied Math., 35, pp. 209–273 (1982).
Chung, K. L. and Rao, M., Feynman-Kac Functional and the Schrödinger Equation, Seminar on Stochastic Processes 1981, Birkhauser, Boston, pp. 1–29 (1981).
Kato, T., Schrödinger Operators with Singular Potentials, Is. J. Math., 13, pp. 135–148 (1973).
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© 1990 Birkhäuser Boston
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Pop-Stojanović, Z.R., Rao, M. (1990). Continuity of Solutions of Schrödinger Equation. In: Çinlar, E., Chung, K.L., Getoor, R.K., Fitzsimmons, P.J., Williams, R.J. (eds) Seminar on Stochastic Processes, 1989. Progress in Probability, vol 18. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3458-6_11
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DOI: https://doi.org/10.1007/978-1-4612-3458-6_11
Publisher Name: Birkhäuser Boston
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