Artículo
Higher-order boundary regularity estimates for nonlocal parabolic equations
Fecha de publicación:
10/2018
Editorial:
Springer
Revista:
Calculus Of Variations And Partial Differential Equations
ISSN:
0944-2669
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We establish sharp higher-order Hölder regularity estimates up to the boundary for solutions to equations of the form ∂tu- Lu= f(t, x) in I× Ω where I⊂ R, Ω ⊂ Rn and f is Hölder continuous. The nonlocal operators L that we consider are those arising in stochastic processes with jumps, such as the fractional Laplacian (- Δ) s, s∈ (0 , 1). Our main result establishes that, if f is Cγ is space and Cγ / 2 s in time, and Ω is a C2 , γ domain, then u/ ds is Cs + γ up to the boundary in space and u is C1 + γ / 2 s up the boundary in time, where d is the distance to ∂Ω. This is the first higher order boundary regularity estimate for nonlocal parabolic equations, and is new even for the fractional Laplacian in C∞ domains.
Palabras clave:
Boundary regularity
,
Nonlocal parabolic equations
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Articulos(CCT - MAR DEL PLATA)
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - MAR DEL PLATA
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - MAR DEL PLATA
Citación
Ros Oton, Xavier; Vivas, Hernán Agustín; Higher-order boundary regularity estimates for nonlocal parabolic equations; Springer; Calculus Of Variations And Partial Differential Equations; 57; 5; 10-2018; 1-20
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