Výsledky vyhledávání - "Laurent Véron"

Akademický článek

Weak solutions of semilinear elliptic equations with Leray-Hardy potentials and measure data

Autor: Huyuan Chen, Laurent Véron

Publikováno v: Mathematics in Engineering, Vol 1, Iss 3, Pp 391-418 (2019)

We study existence and stability of solutions of $$ -\Delta u +\frac{\mu}{|x|^{2 }}u+ g(u)= ν \text{ in }\Omega,\ \ \ u=0\text{ on } ∂Ω,$$ where $\Omega$ is a bounded, smooth domain of $\mathbb{ R}^N$, $N\geq 2$, containing the origin, $\mu\geq-

Externí odkaz: https://doaj.org/article/e864ce4aa9cc4421bad71a9521dd6be5

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Elektronická kniha

Nonlinear Second Order Elliptic Equations Involving Measures

Autor: Moshe Marcus, Laurent Véron

In the last 40 years semi-linear elliptic equations became a central subject of study in the theory of nonlinear partial differential equations. On the one hand, the interest in this area is of a theoretical nature, due to its deep relations to other

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Singularities of fractional Emden's equations via Caffarelli-Silvestre extension

Autor: Huyuan Chen, Laurent Véron

We study the isolated singularities of functions satisfying (E) (--$\Delta$) s v$\pm$|v| p--1 v = 0 in $\Omega$\{0}, v = 0 in R N \$\Omega$, where 0 < s < 1, p > 1 and $\Omega$ is a bounded domain containing the origin. We use the Caffarelli-Silvestr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4e1eb4634e0451cf9245a5bdcf20266d

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Qualitative properties of solutions to semilinear elliptic equations from the gravitational Maxwell Gauged O(3) Sigma model

Autor: Huyuan Chen, Hichem Hajaiej, Laurent Véron

Publikováno v: Journal of Functional Analysis
Journal of Functional Analysis, Elsevier, In press

This article is devoted to the study of the following semilinear equation with measure data which originates in the gravitational Maxwell gauged $O(3)$ sigma model, $$-\Delta u + A_0(\prod^k_{j=1}|x-p_j|^{2n_j} )^{-a} \frac{e^u}{(1+e^u)^{1+a}} = 4\pi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5eb180895f31352f94f91c53d9227320
https://hal.archives-ouvertes.fr/hal-02469900v3/document

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Bounds for eigenvalues of the Dirichlet problem for the logarithmic Laplacian

Autor: Huyuan Chen, Laurent Véron

Publikováno v: Advances in Calculus of Variation
Advances in Calculus of Variation, Walter de Gruyter GmbH, In press

We provide bounds for the sequence of eigenvalues $\{\lambda_i(\Omega)\}_i$ of the Dirichlet problem $$ L_\Delta u=\lambda u\ \ {\rm in}\ \, \Omega,\quad\quad u=0\ \ {\rm in}\ \ \mathbb{R}^N\setminus \Omega,$$ where $L_\Delta$ is the logarithmic Lapl

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::613b45378c907277685f354b1f4bbb19
https://hal.archives-ouvertes.fr/hal-02977991

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Boundary singular solutions of a class of equations with mixed absorption-reaction

Autor: Marie-Françoise Bidaut-Véron, Marta Garcia-Huidobro, Laurent Véron

Publikováno v: Mathematics Subject Classification

We study properties of positive functions satisfying (E) --$��$u + u p -- M |$\nabla$u| q = 0 is a domain $��$ or in R N + when p > 1 and 1 < q < min{p, 2}. We concentrate our research on the solutions of (E) vanishing on the boundary except

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5fc0d6175f47c3d69f6af557bfa8c0a2
http://arxiv.org/abs/2007.16097

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Elektronická kniha

Local And Global Aspects Of Quasilinear Degenerate Elliptic Equations: Quasilinear Elliptic Singular Problems

Autor: Laurent Veron

This book is devoted to the study of elliptic second-order degenerate quasilinear equations, the model of which is the p-Laplacian, with or without dominant lower order reaction term. Emphasis is put on three aspects:

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