Regularity for Quasi-Linear p-Laplacian Type Non-Homogeneous Equations in the Heisenberg Group
نویسندگان
چکیده
When 2−1/Q<p≤2, we establish the Cloc0,1 and Cloc1,α-regularities of weak solutions to quasi-linear p-Laplacian type non-homogeneous equations in Heisenberg group Hn, where Q=2n+2 is homogeneous dimension Hn.
منابع مشابه
REGULARITY FOR ENTROPY SOLUTIONS OF PARABOLIC p-LAPLACIAN TYPE EQUATIONS
In this note we give some summability results for entropy solutions of the nonlinear parabolic equation ut − div ap(x,∇u) = f in ]0, T [×Ω with initial datum in L1(Ω) and assuming Dirichlet’s boundary condition, where ap(., .) is a Carathéodory function satisfying the classical Leray-Lions hypotheses, f ∈ L1(]0, T [×Ω) and Ω is a domain in RN . We find spaces of type Lr(0, T ;Mq(Ω)) containing ...
متن کاملRegularity Results for Quasilinear Elliptic Equations in the Heisenberg Group
We prove regularity results for solutions to a class of quasilinear elliptic equations in divergence form in the Heisenberg group H. The model case is the nondegenerate p-Laplacean operator
متن کاملDifferentiability of Solutions for the Non-degenerate P-laplacian in the Heisenberg Group
We propose a direct method to control the first order fractional difference quotients of solutions to quasilinear subelliptic equations in the Heisenberg group. In this way we implement iteration methods on fractional difference quotients to obtain weak differentiability in the T -direction and then second order weak differentiability in the horizontal directions.
متن کاملTHE LAPLACIAN ON p-FORMS ON THE HEISENBERG GROUP
The Novikov-Shubin invariants for a non-compact Riemannian manifold M can be defined in terms of the large time decay of the heat operator of the Laplacian on L p-forms, △p, on M . For the (2n + 1)-dimensional Heisenberg group H2n+1, the Laplacian △p can be decomposed into operators△p,n(k) in unitary representations β̄k which, when restricted to the centre of H, are characters (mapping ω to exp(...
متن کاملα - regularity for p - harmonic functions in the Heisenberg group for p near 2
We prove C1,α regularity for p-harmonic functions in the Heisenberg group for p in a neighborhood of 2.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2022
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math10214129