Then we establish the regularity of very weak solutions of Beltrami system:there exist integrable exponents r 1 and r 2 (1very weak solution f∈W 1,r 1 loc (Ω,R n)of Beltrami system belongs to W 1,r 2 loc (Ω,R n). So f is still a classical weak solution of Beltrami system.
Using Hodge decomposition theorem, this paper obtains W1,q -regularity for very weak solutions to non-homogeneous A-harmonic systems-Di(Aij(x,u,Du))+Bj(x,u,Du) = 0, j = 1,… ,m and generalizes the corresponding results in [6-8].
Using a pointwise inequality for Sobolev functions in terms of maximum function to construct a global Lipschitz continuous test function,the authors obtain uniqueness re- sults for very weak solutions in grand Sobolev space W_0~(θ,p)) (Ω) to non-linear elliptic equation -divA(x,u,Du)=f(x) satisfying certain conditions.
Many interesting results have been obtained for the solutions of harmonic equation and their obstacle problems, however the definition and regularity results for nonhomogeneous elliptic equation (1.1) stall be unknown.
Regularity for very weak solutions to A-harmonic equation
We develop a theory for a general class of very weak solutions to stationary Stokes and Navier-Stokes equations in a bounded domain Ω with boundary ?Ω of class C2,1, corresponding to boundary data in the distribution space W-1/q,q(?Ω), 1>amp;lt;q>amp;lt;∞.
We investigate a class of weak solutions, the so-called very weak solutions, to stationary and nonstationary Navier-Stokes equations in a bounded domain
Very weak solutions of parabolic systems ofp-Laplacian type
We examine the possibility of using NMR and other measurements on very weak solutions of3He in liquid4He to investigate the superfluid phase transition.
By considering each component of vector functions,we transform Beltrami system to a class of elliptic systems of divergence type.Then we establish the regularity of very weak solutions of Beltrami system:there exist integrable exponents r 1 and r 2 (1