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On the singular PDE’s geometry and boundary value problems. (English) Zbl 1180.35012

Summary: A geometric formulation of singular partial differential equations (PDEs) is considered. Surgery techniques and integral bordism groups are utilized, following previous works by Prástaro on PDEs, in order to build global solutions crossing also singular points and to study their stability properties.

MSC:

35A20 Analyticity in context of PDEs
55N22 Bordism and cobordism theories and formal group laws in algebraic topology
57R20 Characteristic classes and numbers in differential topology
58J32 Boundary value problems on manifolds
20H15 Other geometric groups, including crystallographic groups
35J75 Singular elliptic equations
35K67 Singular parabolic equations
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