We consider quite general fully nonlinear mixed Cauchy-Dirichlet problems with a Caputo derivative D-alpha with respect to the time variable and a in (0, 2). Under natural conditions, we show the existence of a local solution u such that D(alpha)u and the second order space derivatives D-xi,D-x j u belong to the class C-alpha theta/2,C-theta ([0, T] x (Omega) over bar), for some T positive, with theta is an element of(0, 1). Moreover, we show the uniqueness of global solutions in the same class of functions.

Guidetti D. (2023). On the Cauchy-Dirichlet problem for fully nonlinear equations with fractional time derivative. REVISTA MATEMATICA COMPLUTENSE, 36(1), 141-162 [10.1007/s13163-021-00415-w].

On the Cauchy-Dirichlet problem for fully nonlinear equations with fractional time derivative

Guidetti D.
2023

Abstract

We consider quite general fully nonlinear mixed Cauchy-Dirichlet problems with a Caputo derivative D-alpha with respect to the time variable and a in (0, 2). Under natural conditions, we show the existence of a local solution u such that D(alpha)u and the second order space derivatives D-xi,D-x j u belong to the class C-alpha theta/2,C-theta ([0, T] x (Omega) over bar), for some T positive, with theta is an element of(0, 1). Moreover, we show the uniqueness of global solutions in the same class of functions.
2023
Guidetti D. (2023). On the Cauchy-Dirichlet problem for fully nonlinear equations with fractional time derivative. REVISTA MATEMATICA COMPLUTENSE, 36(1), 141-162 [10.1007/s13163-021-00415-w].
Guidetti D.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/918392
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