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Obstacle Problems

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Random Obstacle Problems

Part of the book series: Lecture Notes in Mathematics ((LNMECOLE,volume 2181))

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Abstract

In this chapter we introduce the SPDEs with reflection which are studied in detail in the following chapters. The theory at the beginning is purely deterministic: as in the Skorohod Lemma 2.1, we have a driving continuous function (t, x) ↦ w(t, x) which plays the role of an obstacle and we look for a continuous function z ≥ −w which solves a heat equation on the open set {z > −w} and is reflected on − w. Following Nualart and Pardoux [NP92] we give an existence and uniqueness result for solutions to such obstacle problems.

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Authors and Affiliations

  1. Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, Paris, France

    Lorenzo Zambotti

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  1. Lorenzo Zambotti
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Zambotti, L. (2017). Obstacle Problems. In: Random Obstacle Problems. Lecture Notes in Mathematics(), vol 2181. Springer, Cham. https://doi.org/10.1007/978-3-319-52096-4_5

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