Abstract
In this chapter, following Bony–Courrège–Priouret [BCP], we prove the weak and strong maximum principles and Hopf’s boundary point lemma for second-order elliptic Waldenfels operators which play an essential role throughout the book.
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Bony, J.-M., Courrège, P., Priouret, P.: Semi-groupes de Feller sur une variété à bord compacte et problèmes aux limites intégro-différentiels du second ordre donnant lieu au principe du maximum. Ann. Inst. Fourier (Grenoble) 18, 369–521 (1968)
Fefferman, C., Phong, D.H.: Subelliptic eigenvalue problems. In: Conference on Harmonic Analysis (1981: Chicago), pp. 590–606. Wadsworth, Belmont (1983)
Folland, G.B.: Real Analysis: Modern Techniques and Their Applications, 2nd edn. Wiley, New York (1999)
Hopf, E.: A remark on linear elliptic differential equations of second order. Proc. Am. Math. Soc. 3, 791–793 (1952)
Oleĭnik, O.A.: On properties of solutions of certain boundary problems for equations of elliptic type. Mat. Sbornik 30, 595–702 (1952, in Russian)
Protter, M.H., Weinberger, H.F.: Maximum Principles in Differential Equations. Prentice-Hall, Englewood Cliffs (1967)
Taira, K.: Diffusion Processes and Partial Differential Equations. Academic, Boston (1988)
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Taira, K. (2014). Waldenfels Operators and Maximum Principles. In: Semigroups, Boundary Value Problems and Markov Processes. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43696-7_8
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DOI: https://doi.org/10.1007/978-3-662-43696-7_8
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