Feller Semigroups with a First Order Ventcel’ Boundary Condition

Kazuaki Taira ()
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Kazuaki Taira: University of Tsukuba, The College of Mathematics

Chapter Chapter 25 in Real Analysis Methods for Markov Processes, 2024, pp 645-658 from Springer

Abstract: Abstract Chapter 25 is devoted to the proof of Theorem 1.1 . Namely, we prove that the closed realization $$\mathfrak {A}_{L}$$ A L is the $$\overline{LH_{\alpha }}$$ L H α ¯ infinitesimal generator of a Feller semigroup on $$C(\overline{\Omega })$$ C ( Ω ¯ ) corresponding to such a diffusion phenomenon that a Markovian particle moves by continuous paths in the state space, with absorption, reflection, drift and sticking phenomena at the boundary. Moreover, we prove Remark 1.2 , that is, the domain $$D\left( \mathfrak {A}_{L}\right) $$ D A L does not depend on p, for $$N

Date: 2024
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DOI: 10.1007/978-981-97-3659-1_25

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