Regularity for Weak Solutions to First-Order Local Mean Field Games

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Alharbi, Abdulrahman, Gomes, Diogo, Di Fazio, Giuseppe, Ucer, Melih
Format:	Preprint
Published:	2024
Subjects:	Analysis of PDEs 35Q89 (Primary) 35B65 (Secondary)
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Corruption via Mean Field Games
by: Klibanov, Michael V., et al.
Published: (2025)

Mean Field Games of Controls with Fractional Laplacian
by: Graber, P. Jameson, et al.
Published: (2025)

On the nonexistence of NLS breathers
by: Alejo, Miguel Á., et al.
Published: (2024)

Solving Mean-Field Games with Monotonicity Methods in Banach Spaces
by: Ferreira, Rita, et al.
Published: (2025)

Transporting a Dirac mass in a mean field planning problem
by: Cardaliaguet, Pierre, et al.
Published: (2025)

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations
by: Magaña, Marc, et al.
Published: (2026)

A Fully-discrete Semi-Lagrangian scheme for a price formation MFG model
by: Ashrafyan, Yuri, et al.
Published: (2024)

Endpoint Strichartz estimates for the Schrödinger equation on an exterior domain
by: Georgiev, Vladimir, et al.
Published: (2019)

On special properties of solutions to Camassa-Holm equation and related models
by: Hong, Christian, et al.
Published: (2024)

The evolving surface Cahn-Hilliard equation with a degenerate mobility
by: Elliott, Charles M., et al.
Published: (2024)

Local Wellposedness and Global Weak Solutions of the Pauli-Darwin/Poisswell Equations
by: Germain, Pierre, et al.
Published: (2025)

Regularity and long-time behavior of global weak solutions to a coupled Cahn-Hilliard system: the off-critical case
by: Ouyang, Bohan
Published: (2024)

Stability of dispersive boundary layers for scalar conservation laws in one space dimension
by: Antonelli, Paolo, et al.
Published: (2026)

Global Well-Posedness for the Benjamin-Ono Equation with Small Periodic Initial Data in Analytic Spaces
by: Wang, Yubo
Published: (2026)

Discretization and Vanishing Discount Problems for First-order Mean Field Games
by: Iturriaga, Renato, et al.
Published: (2025)

Remarks on Linear Growth of Vorticity Gradients and Support Diameters for 2D Euler Flow in Half-Plane
by: Chen, Shaoqing, et al.
Published: (2026)

A Convergent Numerical Algorithm for $α$-Dissipative Solutions of the Hunter-Saxton Equation
by: Christiansen, Thomas, et al.
Published: (2023)

A conditional Lagrangian clock barrier at the $C^{1,\frac{1}{3}}$ threshold for axisymmetric Euler without swirl
by: Avadanei, Ovidiu-Neculai
Published: (2026)

Optimal regularity at the free boundary in one-dimensional first-order mean field games
by: Munoz, Sebastian
Published: (2026)

Normal trace inequalities and decay of solutions to the nonlinear Maxwell system with absorbing boundary
by: Nutt, Richard, et al.
Published: (2026)

Rate of convergence for numerical $α$-dissipative solutions of the Hunter-Saxton equation
by: Christiansen, Thomas, et al.
Published: (2024)

Strichartz estimates in Wiener amalgam spaces for Schrödinger equations with at most quadratic potentials
by: Takizawa, Shun
Published: (2025)

Schauder-type estimates and applications
by: Kichenassamy, Satyanad
Published: (2025)

Long-time behaviour of deterministic Mean Field Games with non-monotone interactions
by: Bardi, Martino, et al.
Published: (2023)

Boundedness of weak solutions to degenerate Kolmogorov equations of hypoelliptic type in bounded domains
by: Hou, Mingyi
Published: (2024)

Regularization of Stationary Second-order Mean Field Game Partial Differential Inclusions
by: Osborne, Yohance A. P., et al.
Published: (2024)

A semi-Lagrangian scheme for First-Order Mean Field Games based on monotone operators
by: Carlini, Elisabetta, et al.
Published: (2025)

Stability of bound states for regularized nonlinear Schrödinger equations
by: Albert, John, et al.
Published: (2024)

Resolvent approaches to elliptic regularity in stationary Fokker-Planck equations
by: Lee, Haesung
Published: (2026)

Stability of the spatially homogeneous Landau equation in relative entropy and applications to score-based numerical methods
by: Ilin, Vasily
Published: (2025)

Instantaneous regularization of measure-valued population densities in a Keller--Segel system with flux limitation
by: Kohatsu, Shohei
Published: (2024)

Well-posedness for the NLS hierarchy
by: Adams, Joseph
Published: (2024)

Well-posedness for the dNLS hierarchy
by: Adams, Joseph
Published: (2025)

Global dynamics above the ground state for the energy-critical Hartree equation with radial data
by: Li, Xuemei, et al.
Published: (2025)

A Model Problem for First Order Mean Field Games with Discrete Initial Data
by: Graber, P. Jameson, et al.
Published: (2024)

Regularity theory for fully nonlinear equations of porous medium-type
by: Yun, Hyungsung
Published: (2024)

Analytical Solutions of 3D Maxwell's Equations via Infinite-Order Curl-Operator Expansions
by: Ge, David Wei
Published: (2026)

On the convergence rates of generalized conditional gradient method for fully discretized Mean Field Games
by: Nakamura, Haruka, et al.
Published: (2026)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
language	"en"
VUFIND_SESSION	"1464e6a551e06965ff4dd04abc9be955"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1791183273.5137 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "1464e6a551e06965ff4dd04abc9be955" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; language=en; VUFIND_SESSION=1464e6a551e06965ff4dd04abc9be955"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.58"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"59933"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2411_15174/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2411_15174/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1791183273.5047
REQUEST_TIME	1791183273

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
language	"en"
VUFIND_SESSION	"1464e6a551e06965ff4dd04abc9be955"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1791183273.5137 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "1464e6a551e06965ff4dd04abc9be955" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; language=en; VUFIND_SESSION=1464e6a551e06965ff4dd04abc9be955"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.58"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"59933"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2411_15174/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2411_15174/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1791183273.5047
REQUEST_TIME	1791183273

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: