Local Hölder continuity of nonnegative weak solutions of inverse variation-inequality problems of non-divergence type

Autor:	Yan Dong
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	variation-inequality problems non-divergence parabolic operator existence hölder continuity Mathematics QA1-939 Applied mathematics. Quantitative methods T57-57.97
Zdroj:	Electronic Research Archive, Vol 32, Iss 1, Pp 473-485 (2024)
Druh dokumentu:	article
ISSN:	2688-1594
DOI:	10.3934/era.2024023?viewType=HTML
Popis:	Compared to the standard variational inequalities, inverse variational inequalities are more suitable for pricing American options with indefinite payoff. This paper investigated the initial-boundary value problem of inverse variational inequalities constituted by a class of non-divergence type parabolic operators. We established the existence and Hölder continuity of weak solutions. Since the comparison principle in the case of standard variational inequalities is no longer applicable, we constructed an integral inequality using differential inequalities to determine the global upper bound of the solution. By combining it with the continuous method, we obtained the existence of weak solutions. Additionally, by employing truncation factors, we obtained the lower bound of weak solutions in the cylindrical subdomain, thereby obtaining the Hölder continuity.
Databáze:	Directory of Open Access Journals
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