@inbook{c4df53e9a1cd4ed1bbb977317bc235ff,
title = "A Priori Bounds for Stationary Models",
abstract = "We draw upon our earlier results to study stationary MFGs. Here, we illustrate various techniques in three models. First, we use the Bernstein estimates given in Theorem 3.11, to obtain Sobolev estimates for the value function. Next, we consider a congestion problem and show, through a remarkable identity, that m > 0. Finally, we examine an MFG with a logarithmic nonlinearity. This model presents substantial challenges since the logarithm is not bounded from below. However, a clever integration by parts argument gives the necessary bounds for its study.",
keywords = "Bernstein Estimates, Logarithmic Nonlinearity, Present Substantial Challenges, Priori Bounds, Remarkable Identity",
author = "Gomes, {Diogo A.} and Pimentel, {Edgard A.} and Vardan Voskanyan",
note = "Publisher Copyright: {\textcopyright} 2016, Springer International Publishing Switzerland.",
year = "2016",
doi = "10.1007/978-3-319-38934-9_7",
language = "English (US)",
series = "SpringerBriefs in Mathematics",
publisher = "Springer Science and Business Media B.V.",
pages = "97--103",
booktitle = "SpringerBriefs in Mathematics",
address = "Germany",
}