Asymptotic behaviour of Dirichlet eigenvalues for homogeneous Hörmander operators and algebraic geometry approach

Fuente: arXiv

Gespeichert in:

Bibliographische Detailangaben
Hauptverfasser:	Chen, Hua, Chen, Hong-Ge, Li, Jin-Ning
Format:	Preprint
Veröffentlicht:	2022
Schlagworte:	Analysis of PDEs 35P15, 35P20, 35J70
Online-Zugang:	Acceder al recurso
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Ähnliche Einträge

On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic operators
von: Della Pietra, Francesco, et al.
Veröffentlicht: (2017)

Multiple sign-changing solutions for semilinear subelliptic Dirichlet problem
von: Chen, Hua, et al.
Veröffentlicht: (2025)

The anisotropic $\infty$-Laplacian eigenvalue problem with Neumann boundary conditions
von: Piscitelli, Gianpaolo
Veröffentlicht: (2017)

Sharp embedding results and geometric inequalities for Hörmander vector fields
von: Chen, Hua, et al.
Veröffentlicht: (2024)

A weighted eigenvalue problem for mixed local and nonlocal operators with potential
von: Lakshmi, R., et al.
Veröffentlicht: (2024)

Sobolev inequality and its extremal functions for homogeneous Hörmander vector fields
von: Chen, Hua, et al.
Veröffentlicht: (2025)

Convergence rate and uniform Lipschitz estimate in periodic homogenization of high-contrast elliptic systems
von: Fu, Xin, et al.
Veröffentlicht: (2024)

Upper bound on the multiplicity of eigenvalues of the Schödinger-Dirichlet operator in dimension two
von: Choulli, Mourad
Veröffentlicht: (2025)

Weighted Robin eigenvalue problems and nonlinear elliptic equations with general growth in the gradient
von: Della Pietra, Francesco, et al.
Veröffentlicht: (2025)

Several isoperimetric inequalities of Dirichlet and Neumann eigenvalues of the Witten-Laplacian
von: Chen, Ruifeng, et al.
Veröffentlicht: (2024)

On the criticality and the principal eigenvalue of almost periodic elliptic operators
von: Rossi, Luca
Veröffentlicht: (2026)

Asymptotic behaviour for a class of quasilinear cooperative eigenvalue problems
von: Alvarez-Caudevilla, Pablo
Veröffentlicht: (2024)

Threshold Hierarchy for Packet-Scale Boundary Cancellation of Dirichlet Eigenfunctions
von: Alexa, Anton
Veröffentlicht: (2026)

Non-convergence of the principal eigenvalue of elliptic operators for large advection
von: Bai, Xueli, et al.
Veröffentlicht: (2025)

The High Energy Distribution of Scattering Phase Shifts of Schrödinger operators in Hyperbolic Space
von: Barreto, Antônio Sá
Veröffentlicht: (2025)

On eigenvalues problems for the $p(x)$-Laplacian
von: Marcos, Aboubacar, et al.
Veröffentlicht: (2023)

Principal eigenvalue for some elliptic operators with large drift: Neumann boundary conditions
von: Liu, Shuang, et al.
Veröffentlicht: (2024)

First Dirichlet eigenvalue of the weighted 1-Laplacian operator
von: Barbato, R., et al.
Veröffentlicht: (2026)

On the splitting of Neumann eigenvalues in perforated domains
von: Felli, Veronica, et al.
Veröffentlicht: (2026)

On asymptotics of Robin eigenvalues in the Dirichlet limit
von: Ognibene, Roberto
Veröffentlicht: (2024)

Estimates for the first and second Steklov-Dirichlet eigenvalues
von: Sannipoli, Rossano
Veröffentlicht: (2025)

On the second eigenvalue of the infinity Laplacian with Robin boundary conditions
von: Amato, Vincenzo, et al.
Veröffentlicht: (2024)

Conformal composition operators with applications to Dirichlet eigenvalues
von: Deneche, C., et al.
Veröffentlicht: (2025)

Subelliptic $p$-Laplacian spectral problem for Hörmander vector fields
von: Karazym, Mukhtar, et al.
Veröffentlicht: (2023)

The principal eigenvalue problem for a strongly anisotropic second-order elliptic operator
von: Boutillon, Nathanaël
Veröffentlicht: (2023)

Magnetic Neumann problems with Aharonov-Bohm potentials: boundary asymptotics of eigenvalues and splitting phenomena
von: Felli, Veronica, et al.
Veröffentlicht: (2026)

Variational eigenvalues of the subelliptic $p$-Laplacian
von: Karazym, Mukhtar
Veröffentlicht: (2023)

On the first eigenvalue of Liouville-type problems
von: Bartolucci, Daniele, et al.
Veröffentlicht: (2023)

Dirichlet problem for degenerate Hessian quotient type curvature equations
von: Chen, Xiaojuan, et al.
Veröffentlicht: (2024)

Eigenvalue Estimates for $p$-Laplace Problems on Domains Expressed in Fermi Coordinates
von: Brandolini, Barbara, et al.
Veröffentlicht: (2021)

A stability result for the first Robin-Neumann eigenvalue: A double perturbation approach
von: Cito, Simone, et al.
Veröffentlicht: (2023)

On the limit spectrum of a degenerate operator in the framework of periodic homogenization or singular perturbation problems
von: Ammari, Kaïs, et al.
Veröffentlicht: (2023)

Homogenization of the scattered wave and scattering resonances for periodic high-contrast subwavelength resonators
von: Du, Yuxin, et al.
Veröffentlicht: (2025)

On the Ashbaugh-Benguria type conjecture about lower-order Neumann eigenvalues of the Witten-Laplacian
von: Chen, Ruifeng, et al.
Veröffentlicht: (2024)

Time-harmonic elastic scattering by unbounded deterministic and random rough surfaces in three dimensions
von: Hu, Guanghui, et al.
Veröffentlicht: (2024)

Parametric holomorphy of elliptic eigenvalue problems
von: Bahn, Byeong-Ho
Veröffentlicht: (2024)

Inequalities between Dirichlet and Neumann Eigenvalues on Surfaces
von: Hua, Bobo, et al.
Veröffentlicht: (2024)

Sharp estimates for the first $p$-Laplacian eigenvalue and for the $p$-torsional rigidity on convex sets with holes
von: Paoli, Gloria, et al.
Veröffentlicht: (2019)

Spectral theory of the Neumann-Poincaré operator on multi-layer structures and analysis of plasmon mode splitting
von: Deng, Youjun, et al.
Veröffentlicht: (2025)

Families of non-tiling domains satisfying Pólya's conjecture
von: Freitas, Pedro, et al.
Veröffentlicht: (2022)

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
VUFIND_SESSION	"8e9c674bfa6c224f50f0861b8975c5e8"
ui	"standard"
language	"de"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790882306.9974 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "8e9c674bfa6c224f50f0861b8975c5e8" ]`]
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	"VUFIND_SESSION=8e9c674bfa6c224f50f0861b8975c5e8; ui=standard; language=de"
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	"216.73.217.142"
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	"36440"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2203_10450/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2203_10450/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790882306.9884
REQUEST_TIME	1790882306

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler