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Main Authors:	Chowdhury, Indranil, Vondraček, Zoran, Wagner, Vanja
Format:	Preprint
Published:	2025
Subjects:	Analysis of PDEs 35A01 (Primary) 35R11, 31C05, 35J61, 45K05 (Secondary)
Online Access:	https://arxiv.org/abs/2506.13462
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author	Chowdhury, Indranil Vondraček, Zoran Wagner, Vanja
author_facet	Chowdhury, Indranil Vondraček, Zoran Wagner, Vanja
contents	We study the existence of a large solution to a semilinear problem in a bounded open $C^{1,1}$ set for a class of nonlocal operators obtained by an appropriate subordination of the Laplacian. These operators are classical generalisations of the fractional Laplacian. The existence result is shown under a nonlocal version of the Keller-Osserman condition, stated in terms of the subordinator and the source term $f$.
format	Preprint
id	arxiv_https___arxiv_org_abs_2506_13462
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Large solutions to semilinear equations for subordinate Laplacians in $C^{1,1}$ bounded open sets Chowdhury, Indranil Vondraček, Zoran Wagner, Vanja Analysis of PDEs 35A01 (Primary) 35R11, 31C05, 35J61, 45K05 (Secondary) We study the existence of a large solution to a semilinear problem in a bounded open $C^{1,1}$ set for a class of nonlocal operators obtained by an appropriate subordination of the Laplacian. These operators are classical generalisations of the fractional Laplacian. The existence result is shown under a nonlocal version of the Keller-Osserman condition, stated in terms of the subordinator and the source term $f$.
title	Large solutions to semilinear equations for subordinate Laplacians in $C^{1,1}$ bounded open sets
topic	Analysis of PDEs 35A01 (Primary) 35R11, 31C05, 35J61, 45K05 (Secondary)
url	https://arxiv.org/abs/2506.13462

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* * @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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