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Creators/Authors contains: "Borthagaray, Juan Pablo"

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  1. ; ; (, Nonlinear analysis)
    Free, publicly-accessible full text available August 23, 2025
  2. ; ; (, SIAM Journal on Mathematical Analysis)
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  3. ; ; (, SINUM)
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  4. ; ; (, Mathematics in Engineering)
    null (Ed.)
    We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy minimization, and we discretize the latter with piecewise linear finite elements. For the computation of the discrete solutions, we propose and study a gradient flow and a Newton scheme, and we quantify the effect of Dirichlet data truncation. We also present a wide variety of numerical experiments that illustrate qualitative and quantitative features of fractional minimal graphs and the associated discrete problems. 
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  5. ; ; (, Numerische Mathematik)
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  6. ; ; (, Mathematical Models and Methods in Applied Sciences)
    We obtain regularity results in weighted Sobolev spaces for the solution of the obstacle problem for the integral fractional Laplacian [Formula: see text] in a Lipschitz bounded domain [Formula: see text] satisfying the exterior ball condition. The weight is a power of the distance to the boundary [Formula: see text] of [Formula: see text] that accounts for the singular boundary behavior of the solution for any [Formula: see text]. These bounds then serve us as a guide in the design and analysis of a finite element scheme over graded meshes for any dimension [Formula: see text], which is optimal for [Formula: see text]. 
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