Browsing by Author "Milakis, E."

Now showing items 1-12 of 12

    • Article  

      Boundary value problems for quasilinear ODEs 

      Milakis, E. (2005)
      A priori bounds for the quasilinear ordinary differential equations (ODE), are discussed. A priori bounds for the derivative of the solution of one-dimensional p-Laplacian are proved. The global solvability of quasilinear ...
    • Article  

      Divergence form operators in Reifenberg flat domains 

      Milakis, E.; Toro, T. (2010)
      We study the boundary regularity of solutions of elliptic operators in divergence form with C0,α coefficients or operators which are small perturbations of the Laplacian in non-smooth domains. We show that, as in the case ...
    • Article  

      Fully nonlinear phase transition problems with flat free boundaries 

      Milakis, E. (2010)
      In this paper we continue our study, started in [9], on the regularity theory of Stefan-like free boundary problems for a special class of fully nonlinear equations of parabolic type. We prove that degenerate Lipschitz ...
    • Article  

      Harmonic analysis on chord arc domains 

      Milakis, E.; Pipher, J.; Toro, T. (2013)
      In the present paper we study the solvability of the Dirichlet problem for second order divergence form elliptic operators with bounded measurable coefficients which are small perturbations of given operators in rough ...
    • Article  

      On the extension property of reifenberg-flat domains 

      Lemenant, A.; Milakis, E.; Spinolo, L. V. (2014)
      We provide a detailed proof of the fact that any open set whose boundary is sufficiently flat in the sense of Reifenberg is also Jones-flat, and hence it admits an extension operator. We discuss various applications of ...
    • Article  

      On the regularity of optimal sets in mass transfer problems 

      Milakis, E. (2006)
      Given a set Ω ⊂ ℝn with fixed volume and D ⊂ ℝn, we study the regularity of the boundary of a set Ω that minimizes both its perimeter in D and the transportation cost from Ω1 onto Ω. We prove that Ω has almost minimal ...
    • Article  

      Quantitative stability for the first Dirichlet eigenvalue in Reifenberg flat domains in RN 

      Lemenant, A.; Milakis, E. (2010)
      In this paper we prove that if Ω and Ω′ are close enough for the complementary Hausdorff distance and their boundaries satisfy some geometrical and topological conditions then| λ1 - λ1′ | ≤ C | Ω △ Ω′ |frac(α, N) where λ1 ...
    • Article  

      Regularity for fully nonlinear elliptic equations with neumann boundary data 

      Milakis, E.; Silvestre, L. E. (2006)
      We obtain local C , C 1, , and C 2, regularity results up to the boundary for viscosity solutions of fully nonlinear uniformly elliptic second order equations with Neumann boundary conditions.
    • Article  

      Regularity for the nonlinear Signorini problem 

      Milakis, E.; Silvestre, L. (2008)
      We study the regularity of the solution to a fully nonlinear version of the thin obstacle problem. In particular we prove that the solution is C1, α for some small α > 0. This extends a result of Luis Caffarelli of 1979. ...
    • Article  

      Spectral stability estimates for the Dirichlet and Neumann Laplacian in rough domains 

      Lemenant, A.; Milakis, E.; Spinolo, L. V. (2013)
      In this paper we establish new quantitative stability estimates with respect to domain perturbations for all the eigenvalues of both the Neumann and the Dirichlet Laplacian. Our main results follow from an abstract lemma ...
    • Article  

      A stability result for nonlinear Neumann problems in reifenberg flat domains in Rn 

      Lemenant, A.; Milakis, E. (2011)
      In this paper we prove that if ωk is a sequence of Reifenberg-flat domains in RN that converges to ω for the complementary Haus- dorff distance and if in addition the sequence ωk has a "uniform size of holes", then the ...
    • Article  

      Two-phase transition problems for fully nonlinear parabolic equations of second order 

      Milakis, E. (2005)
      In this paper we study an extension of a regularity theory presented by I. Athanasopoulos, L. Caffarelli and S. Salsa in [3], [4], to some fully nonlinear parabolic equations of second order. We investigate a two-phase ...