Dirichlet problem for second order elliptic equations in nondivergence form with continuous coefficients | Vidéo | Carmin.tv

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Dirichlet problem for second order elliptic equations in nondivergence form with continuous coefficients

Apparaît dans la collection : Harmonic analysis and partial differential equations / Analyse harmonique et équations aux dérivées partielles

We investigate the Dirichlet problem for a non-divergence form elliptic operator $L=a^{i j}(x) D_{i j}+b^{i}(x) D_{i}-c(x)$ in a bounded domain of $\mathbb{R}^{d}$. Under certain conditions on the coefficients of $L$, we first establish the existence of a unique Green's function in a ball and derive two-sided pointwise estimates for it. Utilizing these results, we demonstrate the equivalence of regular points for $L$ and those for the Laplace operator, characterized via the Wiener test. This equivalence facilitates the unique solvability of the Dirichlet problem with continuous boundary data in regular domains. Furthermore, we construct the Green's function for $L$ in regular domains and establish pointwise bounds for it.

Informations sur la vidéo

Date de captation 13/06/2024
Date de publication 10/07/2024
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20189603
Citer cette vidéo Kim, Seick (13/06/2024). Dirichlet problem for second order elliptic equations in nondivergence form with continuous coefficients. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20189603
URL https://dx.doi.org/10.24350/CIRM.V.20189603

Domaine(s)

Equations aux dérivées partielles

Bibliographie

DONG, Hongjie, KIM, Dong-ha, et KIM, Seick. The Dirichlet problem for second-order elliptic equations in non-divergence form with continuous coefficients. arXiv preprint arXiv:2402.17948, 2024. - https://doi.org/10.48550/arXiv.2402.17948

Codes MSC

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