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math.AP2024
Partial Differential Equations on Low-Dimensional Structures
Łukasz Chomienia
This thesis pertains to the study of elliptic and parabolic partial differential equations on "thin" structures. The first main objective is to establish the strong and weak low-di…
math.AP2023
Higher regularity of solutions to elliptic equations on low-dimensional structures
Łukasz Chomienia, Michał Fabisiak
This paper aims to establish counterparts of fundamental regularity statements for solutions to elliptic equations in the setting of low-dimensional structures such as, for instanc…
math.AP2023
Parabolic PDEs on low-dimensional structures
Łukasz Chomienia
The paper concerns the theory of parabolic equations on a broad class of closed subsets of Euclidean space possessing a kind of tangent structure. A necessary framework for conside…