Abstract
We show in this paper that maximal Lq-regularity for time-dependent viscous Hamilton-Jacobi equations with unbounded right-hand side and superquadratic γ-growth in the gradient holds in the full range q>(N+2)γ−1γ. Our approach is based on new γ−2γ−1-Hölder estimates, which are consequence of the decay at small scales of suitable nonlinear space and time Hölder quotients. This is obtained by proving suitable oscillation estimates, that also give in turn some Liouville type results for entire solutions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
