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1.
56 p, 800.6 KB The two-phase problem for harmonic measure in VMO / Prats, Martí (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tolsa Domènech, Xavier (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Let Ω +⊂ Rn+1 be an NTA domain and let Ω -= Rn+1\ Ω +¯ be an NTA domain as well. Denote by ω+ and ω- their respective harmonic measures. Assume that Ω + is a δ-Reifenberg flat domain for some δ> 0 small enough. [...]
2020 - 10.1007/s00526-020-01760-2
Calculus of Variations and Partial Differential Equations, Vol. 59, Issue 3 (June 2020) , art. 102  
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2.
52 p, 769.5 KB Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant / Gallegos, Josep M. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Let Ω ⊂ R be a C domain or, more generally, a Lipschitz domain with small Lipschitz constant and A(x) be a d× d uniformly elliptic, symmetric matrix with Lipschitz coefficients. Assume u is harmonic in Ω, or with greater generality u solves div (A(x) ∇ u) = 0 in Ω, and u vanishes on Σ = ∂Ω ∩ B for some ball B. [...]
2023 - 10.1007/s00526-022-02426-x
Calculus of Variations and Partial Differential Equations, Vol. 62, Issue 4 (May 2023) , art. 113  
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