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Modification of balayage spaces by transitions with application to coupling of PDE’s

Published online by Cambridge University Press:  22 January 2016

Wolfhard Hansen
Wolfhard Hansen*
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100 131, D – 33501 Bielefeld, Germany, hansen@mathematik.uni-bielefeld.de
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Abstract

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Modifications of balayage spaces are studied which, in probabilistic terms, correspond to killing and transitions (creation of mass combined with jumps). This is achieved by a modification of harmonic kernels for sufficiently small open sets. Applications to coupling of elliptic and parabolic partial differential equations of second order are discussed.

Keywords

31D0531B1031B3035J5535K50
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 169 , 2003 , pp. 77 - 118
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

References

[Alb95] Albers, K., Störung von Balayageräumen und Konstruktion von Halbgruppen, PhD thesis, Universität Bielefeld (1995).Google Scholar
[BH86] Bliedtner, J. and Hansen, W., Potential Theory - An Analytic and Probabilistic Approach to Balayage, Universitext, Springer, Berlin-Heidelberg-New York-Tokyo, 1986.Google Scholar
[BHH87] Boukricha, A., Hansen, W. and Hueber, H., Continuous solutions of the generalized Schrödinger equation and perturbation of harmonic spaces, Exposition. Math., 5 (1987), 97–135.Google Scholar
[Bon70] Bony, J. M., Opérateurs elliptiques dégénérés associés aux axiomatiques de la théorie du potentiel, Potential Theory, CIME, 1o Ciclo, Stresa 1969 (1970), pp. 69–119.Google Scholar
[Bou79a] Bouleau, N., Couplage de deux semi-groupes droites C. R. Acad. Sci. Paris Sér. A-B, 288 (1979), no. 8, A465–A467.Google Scholar
[Bou79b] Bouleau, N., Semi-groupe triangulaire associé à un espace biharmonique, C. R. Acad. Sci. Paris Sér. A-B, 288 (1979), no. 7, A415–A417.Google Scholar
[Bou80] Bouleau, N., Espaces biharmoniques et couplage de processus de Markov, J. Math. Pures Appl. (9), 59 (1980), no. 2, 187–240.Google Scholar
[Bou81] Bouleau, N., Théorie du potentiel associée à certains systémes différentiels, Math. Ann., 255 (1981), no. 3, 335–350.Google Scholar
[Bou82] Bouleau, N., Perturbation positive d’un semi-groupe droit dans le cas critique. Application à la construction de processus de Harris, Seminar on Potential Theory, Paris, No. 6, Springer, Berlin (1982), pp. 53–87.Google Scholar
[Bou84] Boukricha, A., Espaces biharmoniques, Théorie du Potentiel, Proceedings, Orsay 1983, Lecture Notes in Mathematics 1983, 239 (1984), pp. 116–148.Google Scholar
[CC72] Constantinescu, C. and Cornea, A., Potential Theory on Harmonic Spaces, Grundlehren d. math. Wiss. Springer, Berlin-Heidelberg-New York, 1972.Google Scholar
[CZ96] Chen, Z. Q. and Zhao, Z., Potential theory for elliptic systems, Ann. Prob., 24 (1996), 293–319.Google Scholar
[Han81] Hansen, W., Semi-polar sets and quasi-balayage, Math. Ann., 257 (1981), 495–517.Google Scholar
[Han87] Hansen, W., Balayage spaces - a natural setting for potential theory, Potential Theory - Surveys and Problems, Proceedings, Prague 1987, Lecture Notes 1344 (1987), pp. 98–117.Google Scholar
[Her62] Hervé, R.-M., Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier, 12 (1962), 415–517.Google Scholar
[Her68] Hervé, R.-M., Les fonctions surharmoniques associées à un opérateur elliptique du second ordre à coefficients discontinus, Ann. Inst. Fourier, 19 (1968), no. 1, 305–359.Google Scholar
[HH88] Hansen, W. and Hueber, H., Eigenvalues in potential theory, J. Diff. Equ., 73 (1988), 133–152.Google Scholar
[HM90] Hansen, W. and Ma, Z. M., Perturbation by differences of unbounded potentials, Math. Ann., 287 (1990), 553–569.Google Scholar
[Kro88] Kroeger, P., Harmonic spaces associated with parabolic and elliptic differential operators, Math. Ann., 285 (1988), 393–403.CrossRefGoogle Scholar
[Smy75] Smyrnelis, E. P., Axiomatique des fonctions biharmoniques, Ann. Inst. Fourier (Grenoble), 25 (1975), no. 1, 35–97.Google Scholar
[Smy76] Smyrnelis, E. P., Axiomatique des fonctions biharmoniques, Ann. Inst. Fourier (Grenoble), 26 (1976), no. 3, 1–47.Google Scholar