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Potential and scattering theory on wildly perturbed domains. (English) Zbl 0293.35056


MSC:

35P25 Scattering theory for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations

References:

[1] Agmon, S., Lectures on Elliptic Boundary Value Problems (1965), D. van Nostrand: D. van Nostrand Princeton, New Jersey · Zbl 0151.20203
[2] Beale, J. T., Scattering frequencies of resonators, Comm. Pure Appl. Math., 26, 549-564 (1973) · Zbl 0254.35094
[3] Carleson, L., Selected Problems on Exceptional Sets (1967), Van Nostrand: Van Nostrand New York · Zbl 0189.10903
[4] Courant, R.; Hilbert, D., (Methods of Mathematical Physics, Vol. I (1953), Interscience: Interscience New York) · Zbl 0729.00007
[5] Hunt, G., Some theorems concerning Brownian motion, Trans. Amer. Math. Soc., 81, 294-319 (1956) · Zbl 0070.36601
[6] Kac, M., Probabilistic methods in some problems of scattering theory, Rocky Mountain J. Math., 4, 511-538 (1974) · Zbl 0314.47006
[7] Kac, M., Aspects Probabilistes de la Théorie du Potentiel (1970), Univ. de Montreal: Univ. de Montreal Montreal · Zbl 0216.10205
[8] Kato, T., Perturbation Theory for Linear Operators (1966), Springer-Verlag: Springer-Verlag New York · Zbl 0148.12601
[9] Lax, P.; Phillips, R., Scattering Theory (1967), Academic Press: Academic Press New York · Zbl 0214.12002
[10] Lax, P.; Phillips, R., Scattering theory for the acoustic equation in an even number of space dimensions, Indiana Univ. Math. J., 22, 101-134 (1972) · Zbl 0236.35036
[11] Spitzer, F., Electrostatic capacity, heat flow, and Brownian motion, Z. Wahrscheinlichkeitstheorie, 3, 110-121 (1964) · Zbl 0126.33505
[12] Whiteman, W., (Thesis (1964), Cornell University)
[13] J. Rauch and M. TaylorJ. Math. Phys.; J. Rauch and M. TaylorJ. Math. Phys.
[14] M. Taylor; M. Taylor · Zbl 0336.31005
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