Arshak Petrosyan
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1
Total Citations
30
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1
About
Arshak Petrosyan is a leading figure in geometric measure theory and nonlinear partial differential equations, with a particular emphasis on free boundary problems and sub-elliptic geometry. His foundational work on the obstacle problem in Carnot groups has reshaped our understanding of regularity theory in non-Euclidean settings. In his highly cited 2006 paper, "The sub-elliptic obstacle problem: C^1,α regularity of the free boundary in Carnot groups of step two," Petrosyan established that the free boundary in these degenerate environments is C^1,α smooth—a result that was far from obvious given the underlying sub-Riemannian structure. This breakthrough, which has garnered 30 citations, opened new avenues for analyzing free boundaries in stratified Lie groups and has influenced subsequent research on sub-elliptic PDEs. Petrosyan’s work bridges classical potential theory with modern geometric analysis, providing powerful tools for studying the regularity of interfaces in complex geometries. His contributions are essential reading for anyone interested in the interplay between analysis, geometry, and the fine structure of solutions to degenerate elliptic equations.
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