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The linear elasticity system under singular forces (2310.10866v1)
Published 16 Oct 2023 in math.NA and cs.NA
Abstract: We study the linear elasticity system subject to singular forces. We show existence and uniqueness of solutions in two frameworks: weighted Sobolev spaces, where the weight belongs to the Muckenhoupt class $A_2$; and standard Sobolev spaces where the integrability index is less than $d/(d-1)$; $d$ is the spatial dimension. We propose a standard finite element scheme and provide optimal error estimates in the $\mathbf{L}2$--norm. By proving well posedness, we clarify some issues concerning the study of generalized mixed problems in Banach spaces.