We consider solutions of the equation -Delta u + lambda u + |Delta u|(q) = f, which blow up uniformly at the boundary of a smooth domain, that can be interpreted as the value function of a state constraint control problem for a Brownian motion. We prove a complete asymptotic expansion of the gradient at the boundary, giving the precise behavior of normal and tangent components. The result is achieved by proving Lipschitz regularity for u - S, where S is an explicit singular corrector term. As the main motivation and application of our result, we characterize the behavior of the singular optimal control law and of the constrained dynamics near the boundary.

Leonori, T., Porretta, A. (2007). The boundary behavior of blow-up solutions related to a stochastic control problem with state constraint. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 39(4), 1295-1327 [10.1137/070681363].

The boundary behavior of blow-up solutions related to a stochastic control problem with state constraint

PORRETTA, ALESSIO
2007-01-01

Abstract

We consider solutions of the equation -Delta u + lambda u + |Delta u|(q) = f, which blow up uniformly at the boundary of a smooth domain, that can be interpreted as the value function of a state constraint control problem for a Brownian motion. We prove a complete asymptotic expansion of the gradient at the boundary, giving the precise behavior of normal and tangent components. The result is achieved by proving Lipschitz regularity for u - S, where S is an explicit singular corrector term. As the main motivation and application of our result, we characterize the behavior of the singular optimal control law and of the constrained dynamics near the boundary.
2007
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
Asymptotic expansion; Boundary blow-up solutions; Nonlinear elliptic equations; State constraint problem for the Brownian motion
Leonori, T., Porretta, A. (2007). The boundary behavior of blow-up solutions related to a stochastic control problem with state constraint. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 39(4), 1295-1327 [10.1137/070681363].
Leonori, T; Porretta, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/34858
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