C1,?-regularity for variational problems in the Heisenberg group
نویسندگان
چکیده
We study the regularity of minima scalar variational integrals $p$-growth, $1<p<\infty$, in Heisenberg group and prove H\"older continuity horizontal gradient minima.
منابع مشابه
Regularity 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 کاملC1-regularity of solutions for p-Laplacian problems
In this work, we study C 1-regularity of solutions for one-dimensional p-Laplacian problems and systems with a singular weight which may not be in L 1. On the basis of the regularity result, we give an example to show the multiplicity of positive (or negative) solutions as well as sign-changing solutions especially when the nonlinear term is p-superlinear.
متن کاملInterior gradient regularity for BV minimizers of singular variational problems
We consider a class of vectorial integrals with linear growth, where, as a key feature, some degenerate/singular behavior is allowed. For generalized minimizers of these integrals in BV, we establish interior gradient regularity and — as a consequence — uniqueness up to constants. In particular, these results apply, for 1 < p < 2, to the singular model integrals ∫ Ω (1 + |∇w(x)|) 1 p dx . MSC (...
متن کاملHartley Series Direct Method for Variational Problems
The computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. In this approach, a truncated Hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. Two illustrative...
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: Analysis & PDE
سال: 2021
ISSN: ['2157-5045', '1948-206X']
DOI: https://doi.org/10.2140/apde.2021.14.567