TY - JOUR
T1 - Viscosity solutions to inhomogeneous Aronsson’s equations involving Hamiltonians ⟨ A(x) p, p⟩
AU - Lu, Guozhen
AU - Miao, Qianyun
AU - Zhou, Yuan
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/2/1
Y1 - 2019/2/1
N2 - We consider inhomogeneous Aronsson’s equation [Figure not available: see fulltext.] where U is a bounded domain of Rn with n≥ 2 , A∈ C1(U; Rn × n) is symmetric and uniformly elliptic, and f∈ C(U). First, we establish the existence and uniqueness of viscosity solutions for the corresponding Dirichlet problem on subdomains. Then we obtain the local Lipschitz regularity and the linear approximation property of viscosity solutions to (0.1). Moreover, under additional assumptions that A∈ C1 , 1(U; Rn × n) and f∈ C0 , 1(U) , we prove the everywhere differentiability of viscosity solutions to (0.1).
AB - We consider inhomogeneous Aronsson’s equation [Figure not available: see fulltext.] where U is a bounded domain of Rn with n≥ 2 , A∈ C1(U; Rn × n) is symmetric and uniformly elliptic, and f∈ C(U). First, we establish the existence and uniqueness of viscosity solutions for the corresponding Dirichlet problem on subdomains. Then we obtain the local Lipschitz regularity and the linear approximation property of viscosity solutions to (0.1). Moreover, under additional assumptions that A∈ C1 , 1(U; Rn × n) and f∈ C0 , 1(U) , we prove the everywhere differentiability of viscosity solutions to (0.1).
UR - http://www.scopus.com/inward/record.url?scp=85057579752&partnerID=8YFLogxK
U2 - 10.1007/s00526-018-1460-5
DO - 10.1007/s00526-018-1460-5
M3 - Article
AN - SCOPUS:85057579752
SN - 0944-2669
VL - 58
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 1
M1 - 8
ER -