Differentiability of Solutions for the Non-degenerate P-laplacian in the Heisenberg Group

نویسنده

  • ANDRÁS DOMOKOS
چکیده

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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The fibering map approach to a quasilinear degenerate p(x)-Laplacian equation

‎By considering a degenerate $p(x)-$Laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent Sobolev space is presented‎. ‎Multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding Nehari manifold‎. 

متن کامل

Translation invariant surfaces in the 3-dimensional Heisenberg‎ ‎group

‎In this paper‎, ‎we study translation invariant surfaces in the‎ ‎3-dimensional Heisenberg group $rm Nil_3$‎. ‎In particular‎, ‎we‎ ‎completely classify translation invariant surfaces in $rm Nil_3$‎ ‎whose position vector $x$ satisfies the equation $Delta x = Ax$‎, ‎where $Delta$ is the Laplacian operator of the surface and $A$‎ ‎is a $3 times 3$-real matrix‎.

متن کامل

Triple positive solutions of $m$-point boundary value problem on time scales with $p$-Laplacian

‎In this paper‎, ‎we consider the multipoint boundary value problem for one-dimensional $p$-Laplacian‎ ‎dynamic equation on time scales‎. ‎We prove the existence at least three positive solutions of the boundary‎ ‎value problem by using the Avery and Peterson fixed point theorem‎. ‎The interesting point is that the non-linear term $f$ involves a first-order derivative explicitly‎. ‎Our results ...

متن کامل

A note on critical point and blow-up rates for singular and degenerate parabolic equations

In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

متن کامل

C 1 , α local regularity for the solutions of the p - Laplacian on the Heisenberg group . The case 1 + 1 √ 5 < p ≤ 2

We prove the Hölder continuity of the homogeneous gradient of the weak solutions u ∈ W 1,p loc of the p-Laplacian on the Heisenberg group Hn, for 1+ 1 √ 5 < p ≤ 2.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007