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Bibliographic Details
Main Author:	Maione, Alberto
Format:	Preprint
Published:	2025
Subjects:	Functional Analysis Analysis of PDEs
Online Access:	https://arxiv.org/abs/2509.14703
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On the eigenvalues and Fuč\'ık spectrum of $p$-Laplace local and nonlocal operator with mixed interpolated Hardy term
by: Malhotra, Shammi, et al.
Published: (2025)

Fractional Sobolev spaces related to an ultraparabolic operator
by: Pesce, Antonello, et al.
Published: (2025)

Fractional weighted Sobolev spaces associated to the Riesz fractional gradient
by: García-Sáez, Guillermo
Published: (2025)

Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces and their applications
by: Ikeda, Masahiro, et al.
Published: (2024)

Sobolev inequality and its applications to nonlinear PDE on noncommutative Euclidean spaces
by: Ruzhansky, Michael, et al.
Published: (2024)

Sobolev inequalities for canceling operators
by: Breit, Dominic, et al.
Published: (2025)

Equivalence of Sobolev norms in Lebesgue spaces for Hardy operators in a half-space
by: Bui, The Anh, et al.
Published: (2023)

Fractional operators and Sobolev spaces on homogeneous groups
by: Garofalo, Nicola, et al.
Published: (2026)

Ciarlet Nečas condition in fractional Sobolev spaces
by: Hencl, Stanislav, et al.
Published: (2026)

Zero-extension convergence and Sobolev spaces on changing domains
by: Evseev, Nikita, et al.
Published: (2024)

Theory of capacities in fracional Sobolev spaces with variable exponents
by: Baalal, Azeddine, et al.
Published: (2019)

Analysis of Solow-Swan model with nonlocal fractional derivative operator
by: Aibinu, MO, et al.
Published: (2025)

Poincaré-Sobolev equations with the critical exponent and a potential in the hyperbolic space
by: Bhakta, Mousomi, et al.
Published: (2024)

Korevaar-Schoen and heat kernel characterizations of Sobolev and BV spaces on local trees
by: Baudoin, Fabrice, et al.
Published: (2025)

Homogeneous Sobolev and Besov spaces on special Lipschitz domains and their traces
by: Gaudin, Anatole
Published: (2023)

Equivalence of Sobolev norms for Kolmogorov operators with scaling-critical drift
by: Bui, The Anh, et al.
Published: (2024)

Jumps in Besov spaces and fine properties of Besov and fractional Sobolev functions
by: Hashash, Paz, et al.
Published: (2023)

A characterization of the subspace of radially symmetric functions in Sobolev spaces
by: Ostermann, Matthias
Published: (2022)

Multilinear paraproducts on Sobolev spaces
by: Di Plinio, Francesco, et al.
Published: (2024)

Capacitary inradius and Poincaré-Sobolev inequalities
by: Bozzola, Francesco, et al.
Published: (2024)

Sobolev inequalities for nonlinear Dirichlet forms
by: Chill, Ralph, et al.
Published: (2026)

Gamma-convergence of nonlocal energies for partitions
by: Gabard, Thomas, et al.
Published: (2025)

Particle approximation of nonlocal interaction energies
by: Carazzato, Davide, et al.
Published: (2025)

Solutions to Sobolev Supercritical Nonlinear Schrodinger Equations on an Annulus via a Hopf Reduction Method
by: Liang, Jian, et al.
Published: (2025)

Sobolev embeddings for kinetic Fokker-Planck equations
by: Pascucci, Andrea, et al.
Published: (2022)

A simple proof of attainability for the Sobolev inequality
by: Sano, Megumi
Published: (2024)

Relations between Kondratiev spaces and refined localization Triebel-Lizorkin spaces
by: Hansen, Markus, et al.
Published: (2024)

Classification of positive solutions to the Hénon-Sobolev critical systems
by: Zhou, Yuxuan, et al.
Published: (2023)

Characterizations of Lorentz Type Sobolev Multiplier Spaces and Their Preduals
by: Ooi, Keng Hao
Published: (2026)

Sharp quantitative stability for the fractional Sobolev trace inequality
by: Zhang, Yingfang, et al.
Published: (2023)

Complex interpolation of power-weighted Sobolev spaces with boundary conditions
by: Roodenburg, Floris B.
Published: (2025)

The vanishing discount problem for nonlocal Hamilton-Jacobi equations
by: Davini, Andrea, et al.
Published: (2025)

Extrapolation of compactness on weighted mixed Lebesgue spaces
by: Carro, María J., et al.
Published: (2025)

Classification Theorem For Positive Critical Points Of Sobolev Trace Inequality
by: Zhou, Yang
Published: (2024)

Extremals for sharp Poincaré-Sobolev inequalities: periodically perforated sets and beyond
by: Brasco, Lorenzo, et al.
Published: (2025)

Extremal functions for a supercritical k-Hessian inequality of Sobolev-type
by: de Oliveira, José Francisco, et al.
Published: (2020)

Logarithmic Sobolev Inequalities for Bounded Domains and Applications to Drift-Diffusion Equations
by: Abdo, Elie, et al.
Published: (2024)

Quality of non-compactness for Sobolev Embedding with one point non-compactness
by: Chuah, Chian Yeong, et al.
Published: (2023)

Homogenization of parabolic problems for non-local convolution type operators under non-diffusive scaling of coefficients
by: Piatnitski, Andrey, et al.
Published: (2025)

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'

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