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Creators/Authors contains: "Engelstein, Max"

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  1. ; ; ( , Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract

    We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers, in the salient dimensions, a one-phase free boundary analogue of Bernstein’s problem for minimal surfaces.As an application, we also classify monotone solutions of semilinear equations with a bump-type nonlinearity.

     
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    Free, publicly-accessible full text available October 27, 2024
  2. ; ; ; ( , Forum of Mathematics, Sigma)
    Abstract We study the existence and structure of branch points in two-phase free boundary problems. More precisely, we construct a family of minimizers to an Alt–Caffarelli–Friedman-type functional whose free boundaries contain branch points in the strict interior of the domain. We also give an example showing that branch points in the free boundary of almost-minimizers of the same functional can have very little structure. This last example stands in contrast with recent results of De Philippis, Spolaor and Velichkov on the structure of branch points in the free boundary of stationary solutions. 
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  3. ; ; ( , Transactions of the American Mathematical Society)
    On any closed Riemannian manifold of dimension , we prove that if a function nearly minimizes the Yamabe energy, then the corresponding conformal metric is close, in a quantitative sense, to a minimizing Yamabe metric in the conformal class. Generically, this distance is controlled quadratically by the Yamabe energy deficit. Finally, we produce an example for which this quadratic estimate is false. 
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  4. ; ; ( , Journal of the European Mathematical Society)
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  5. ; ( , Ars inveniendi analytica)
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  6. ; ; ; ; ( , Indiana University Mathematics Journal)
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  7. ; ; ; ( , Mathematische Zeitschrift)
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  8. ; ; ; ; ( , Communications on Pure and Applied Mathematics)
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  9. ; ; ( , Duke Mathematical Journal)
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  10. ; ; ( , Duke Mathematical Journal)
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