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Pré-Publication, Document De Travail Année : 2024

On the $H^{m}$-Regularity for Second Order Elliptic Equations

Subham De

Résumé

This article serves as one of the integral topics of my Masters Thesis under the kind supervision of Prof. K. Sreenadh at IIT Delhi, India. Our primary objective in this paper is to discuss the $H^{m}$-Regularity for second order elliptic equations over Sobolev Spaces. We here consider the cases $m=1$ and $m\geq 2$ separately. We revisit some elementary concepts in \textit{Functional Analysis} and \textit{Abstract Harmonic Analysis} before providing a proper definiton to the notion of weak solution of a Dirichlet Problem.\par While towards the later stages, we shall classify different types of regularity conditions, the main focus lies upon deducing appropriate ellipticity conditions in support of commenting about the existence and uniqueness of the weak solutions to a given problem. Appropriate references are provided in the bibliography section to facilitate further reading for ardent readers and researchers in this field.
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Dates et versions

hal-04477849 , version 1 (26-02-2024)
hal-04477849 , version 2 (28-02-2024)
hal-04477849 , version 3 (07-03-2024)

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  • HAL Id : hal-04477849 , version 1

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Subham De. On the $H^{m}$-Regularity for Second Order Elliptic Equations. 2024. ⟨hal-04477849v1⟩
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