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Award ID contains: 2000041

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  1. ; (, Analysis & PDE)
    Full Text Available 
  2. ; (, Mathematics in Engineering)
    null (Ed.)
    Full Text Available 
  3. ; ; (, Archive for Rational Mechanics and Analysis)
    null (Ed.)
    We study the existence, uniqueness, and optimal regularity of solutions to trans-mission problems for harmonic functions with C1,α interfaces. For this, we develop a novel geometric stability argument based on the mean value property. 
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    Accepted Manuscript Full Text Available
  4. ; ; (, Communications in Partial Differential Equations)
    null (Ed.)
    Full Text Available 
  5. ; ; (, Communications in Partial Differential Equations)
    null (Ed.)
    Full Text Available 
  6. ; ; (, Archive for Rational Mechanics and Analysis)
    null (Ed.)
    Abstract We study optimal regularity and free boundary for minimizers of an energy functional arising in cohesive zone models for fracture mechanics. Under smoothness assumptions on the boundary conditions and on the fracture energy density, we show that minimizers are $$C^{1, 1/2}$$ C 1 , 1 / 2 , and that near non-degenerate points the fracture set is $$C^{1, \alpha }$$ C 1 , α , for some $$\alpha \in (0, 1)$$ α ∈ ( 0 , 1 ) . 
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  7. (, Algebra i analiz)
    null (Ed.)
    The goal of this work is to explain an unexpected feature of the expanding level sets of the solutions of a system where a half-plane in which reaction-diffusion phenomena take place exchanges mass with a line having a large diffusion of its own. The system was proposed by H. Berestycki, L. Rossi and the second author as a model of enhancement of biological invasions by a line of fast diffusion. It was observed numerically by A.-C. Coulon that the leading edge of the front, rather than being located on the line, was in the lower half-plane. We explain this behavior for a closely related free boundary problem. We construct travelling waves for this problem, and the analysis of their free boundary near the line confirms the predictions of the numerical simulations. 
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    Accepted Manuscript Full Text Available