Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Vardan Voskanyan"'
We obtain sharp local $C^{1,\alpha}$ regularity of solutions for singular obstacle problems, Euler-Lagrange equation of which is given by $$ \Delta_p u=\gamma(u-\varphi)^{\gamma-1}\,\text{ in }\,\{u>\varphi\}, $$ for $0\varphi\}$, we prove optimal $C
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::88b37fe06d26d6330dc0cbab39960e34
http://arxiv.org/abs/2210.09413
http://arxiv.org/abs/2210.09413
In this paper we consider a mean field optimal control problem with an aggregation–diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a Hamilton
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e193bb6f31b3bbcaae5f7058cb3414c2
http://arxiv.org/abs/1909.10596
http://arxiv.org/abs/1909.10596
Autor:
Vardan Voskanyan, Diogo A. Gomes
Publikováno v:
SIAM Journal on Control and Optimization. 54:1030-1055
In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is pa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::95440a86c7733fb14403aa2a79636fef
https://doi.org/10.1137/130944503
https://doi.org/10.1137/130944503
Autor:
Vardan Voskanyan, Diogo A. Gomes
Publikováno v:
Journal of the London Mathematical Society. 92:778-799
We consider time-dependent mean-field games with congestion that are given by a system of a Hamilton-Jacobi equation coupled with a Fokker-Planck equation. The congestion effects make the Hamilton-Jacobi equation singular. These models are motivated
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::35c71e155bf11b0b4ec5a26900f19554
https://doi.org/10.1112/jlms/jdv052
https://doi.org/10.1112/jlms/jdv052
Mean-field games (MFGs) are models for large populations of competing rational agents that seek to optimize a suitable functional. In the case of congestion, this functional takes into account the difficulty of moving in high-density areas. Here, we
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f0dcb13da30ee01ad216ee6c40c0132a
http://arxiv.org/abs/1710.01566
http://arxiv.org/abs/1710.01566
Publikováno v:
Nonlinear Analysis: Theory, Methods & Applications. 99:49-79
In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gom
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::aeb653cd8dd9b51ad997878f29017209
https://doi.org/10.1016/j.na.2013.12.016
https://doi.org/10.1016/j.na.2013.12.016
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems,
Publikováno v:
SpringerBriefs in Mathematics ISBN: 9783319389325
Here, we discuss two problems—an MFG with a logarithmic nonlinearity and an MFG with congestion effects. Stationary versions of these two problems were considered in Chap. 7 However, the techniques for time-dependent problems are substantially diff
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https://explore.openaire.eu/search/publication?articleId=doi_________::0030752360e98d8520979d2781c83c8b
https://doi.org/10.1007/978-3-319-38934-9_9
https://doi.org/10.1007/978-3-319-38934-9_9
Publikováno v:
SpringerBriefs in Mathematics ISBN: 9783319389325
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2ffb23e67caad859e68a31eb6e390e4b
https://doi.org/10.1007/978-3-319-38934-9
https://doi.org/10.1007/978-3-319-38934-9
Publikováno v:
SpringerBriefs in Mathematics ISBN: 9783319389325
In this last chapter, we address the existence problem for local mean-field games. First, we illustrate the bootstrapping technique and put together the previous estimates. Thanks to this technique, we show that solutions of stationary MFGs are bound
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dddd807b1a40287d07cf6f6cbf7f03ad
https://doi.org/10.1007/978-3-319-38934-9_11
https://doi.org/10.1007/978-3-319-38934-9_11