2015/12/07 by Disson dos Prazeres, Eduardo V. Teixeira, Prazeres, Disson dos +1
Computer Science · Mathematics · #35B65 #35R35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1512.02002
openalex publication_date 2015/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study cavitation type equations, div(aij(X) ∇ u) ∼ δ0(u), for bounded, measurable elliptic media aij(X). De Giorgi-Nash-Moser theory assures that solutions are α-Hölder continuous within its set of positivity, \u>0\, for some exponent α strictly less than one. Notwithstanding, the key, main result proven in this paper provides a sharp Lipschitz regularity estimate for such solutions along their free boundaries, ∂ \u>0 \. Such a sharp estimate implies geometric-measure constrains for the free boundary. In particular, we show that the non-coincidence \u>0\ set has uniform positive density and that the free boundary has finite (n- ς)-Hausdorff measure, for a universal number 0< ς≤ 1.