Eero Saarinem

Eero Saarine

Eero Saarinen

Eero Saarinen was a Finnish-American architect and industrial designer during the 1940s and 1950s. He designed many famous and recognizable buildings, such as the CBS Building and the Dulles Airport. He focused heavily on having a fully thought out and developed concept. His concepts always shined the message in his projects

Uus teadusdoktor Eero Merilind

Eesti Arst 2016; 95(8):55

Local regularity results for value functions of tug-of-war with noise and running payoff

We prove local Lipschitz continuity and Harnack's inequality for value functions of the stochastic game tug-of-war with noise and running payoff. As a consequence, we obtain game-theoretic proofs for the same regularity properties for viscosity solutions of the inhomogeneous $p$-Laplace equation when $p>2$.Comment: 20 pages. Some misprints corrected. To appear in Adv. Calc. Va

A hunt for sharp LpL ^p-estimates and rank-one convex variational integrals

Learning how to figure out sharp $L^p$-estimates of nonlinear differential expressions, to prove and use them, is a fundamental part of the development of PDEs and Geometric Function Theory (GFT). Our survey presents, among what is known to date, some notable recent efforts and novelties made in this direction. We focus attention here on the historic Morrey's Conjecture and Burkholder's martingale inequalities for stochastic integrals. Some of these topics have already been discussed by the present authors [5] and by Rodrigo Ba\~{n}uelos [10]. Nevertheless, there is always something new to add.Comment: 24 page