scholarly journals Hölder Regularity for Viscosity Solutions of Fully Nonlinear, Local or Nonlocal, Hamilton–Jacobi Equations with Superquadratic Growth in the Gradient

2011 ◽  
Vol 49 (2) ◽  
pp. 555-573 ◽  
Author(s):  
Pierre Cardaliaguet ◽  
Catherine Rainer
Keyword(s):  
Viscosity Solutions ◽  
Hölder Regularity ◽  
Fully Nonlinear ◽  
Superquadratic Growth ◽  
Jacobi Equations ◽  
Holder Regularity

scholarly journals Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian

2018 ◽  
Vol 20 (04) ◽  
pp. 1750035 ◽  
Author(s):  
Amal Attouchi ◽  
Mikko Parviainen
Keyword(s):  
Evolution Equation ◽  
Viscosity Solutions ◽  
Source Term ◽  
Divergence Form ◽  
Hölder Regularity ◽  
Spatial Gradient ◽  
War Games ◽  
Holder Regularity ◽  
Continuous Source

In this paper, we study an evolution equation involving the normalized [Formula: see text]-Laplacian and a bounded continuous source term. The normalized [Formula: see text]-Laplacian is in non-divergence form and arises for example from stochastic tug-of-war games with noise. We prove local [Formula: see text] regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration.

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