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Creators/Authors contains: "Petrosyan, Arshak"

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  1. ; (, Calculus of Variations and Partial Differential Equations)
    null (Ed.)
    Full Text Available 
  2. ; ; ; (, Calculus of Variations and Partial Differential Equations)
    Abstract We study the singular set in the thin obstacle problem for degenerate parabolic equations with weight$$|y|^a$$ | y | a for$$a \in (-1,1)$$ a ∈ ( - 1 , 1 ) . Such problem arises as the local extension of the obstacle problem for the fractional heat operator$$(\partial _t - \Delta _x)^s$$ ( ∂ t - Δ x ) s for$$s \in (0,1)$$ s ∈ ( 0 , 1 ) . Our main result establishes the complete structure and regularity of the singular set of the free boundary. To achieve it, we prove Almgren-Poon, Weiss, and Monneau type monotonicity formulas which generalize those for the case of the heat equation ($$a=0$$ a = 0 ). 
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  3. ; (, Algebra i analiz)
    In this paper we introduce a notion of almost minimizers for certain variational problems governed by the fractional Laplacian, with the help of the Caffarelli-Silvestre extension. In particular, we study almost fractional harmonic functions and almost minimizers for the fractional obstacle problem with zero obstacle. We show that for a certain range of parameters, almost minimizers are almost Lipschitz or C1,β-regular. 
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