This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0...This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0(1,2) (Omega, R(N))\parallel to u parallel to L(D) = 1}. Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Holder continuous.展开更多
In this paper,the author studies the regularity of Munn rings and completely 0- simple semigroup rings.When either(i)R is a ring with identity and I and A are infinite,or(ii) R is a strong IBN and fully Dedekind-finit...In this paper,the author studies the regularity of Munn rings and completely 0- simple semigroup rings.When either(i)R is a ring with identity and I and A are infinite,or(ii) R is a strong IBN and fully Dedekind-finite ring with identity and either I or A is finite,in Section 2,the regularity of the Munn ring M(R;I,A;P)is characterized;in Section 3,for a completely 0-simple semigroup S= M°(G;I,A;P),the regularity of RS is characterized.Meantime,the author shows that for a locally finite monoid S and a ring R with identity,RS is a strong IBN ring if and only if R is so;RS is fully Dedekind-finite if and only if R is so.展开更多
This paper is devoted to the long time behavior of the solution to the initial boundary value problems for a class of the Kirchhoff wave equations with nonlinear strongly damped terms: . Firstly, in order to prove the...This paper is devoted to the long time behavior of the solution to the initial boundary value problems for a class of the Kirchhoff wave equations with nonlinear strongly damped terms: . Firstly, in order to prove the smoothing effect of the solution, we make efficient use of the analytic property of the semigroup generated by the principal operator of the equation in the phase space. Then we obtain the regularity of the global attractor and construct the approximate inertial manifold of the equation. Finally, we prove that arbitrary trajectory of the Kirchhoff wave equations goes into a small neighbourhood of the approximate inertial manifold after large time.展开更多
In this paper,a Littlewood-Paley function characterization of the spaces L p（R）,1〈p〈∞,is first established by means of the equivalent conditions of tight wavelet frames,wherein the Littlewood-Paley function is as...In this paper,a Littlewood-Paley function characterization of the spaces L p（R）,1〈p〈∞,is first established by means of the equivalent conditions of tight wavelet frames,wherein the Littlewood-Paley function is associated with a tight wavelet frame generated by the so-called extension principles.With the above characterization,another characterization of L p（R）,1〈p〈∞,is also established in terms of the weighted l 2-norm of the wavelet frame coefficients,which can be a useful tool in harmonic analysis,approximation theory,and image processing.展开更多
文摘This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0(1,2) (Omega, R(N))\parallel to u parallel to L(D) = 1}. Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Holder continuous.
文摘In this paper,the author studies the regularity of Munn rings and completely 0- simple semigroup rings.When either(i)R is a ring with identity and I and A are infinite,or(ii) R is a strong IBN and fully Dedekind-finite ring with identity and either I or A is finite,in Section 2,the regularity of the Munn ring M(R;I,A;P)is characterized;in Section 3,for a completely 0-simple semigroup S= M°(G;I,A;P),the regularity of RS is characterized.Meantime,the author shows that for a locally finite monoid S and a ring R with identity,RS is a strong IBN ring if and only if R is so;RS is fully Dedekind-finite if and only if R is so.
文摘This paper is devoted to the long time behavior of the solution to the initial boundary value problems for a class of the Kirchhoff wave equations with nonlinear strongly damped terms: . Firstly, in order to prove the smoothing effect of the solution, we make efficient use of the analytic property of the semigroup generated by the principal operator of the equation in the phase space. Then we obtain the regularity of the global attractor and construct the approximate inertial manifold of the equation. Finally, we prove that arbitrary trajectory of the Kirchhoff wave equations goes into a small neighbourhood of the approximate inertial manifold after large time.
基金Supported by the National High Technology Research and Development Program of China (863 Program) (2009AA12Z203,2008AA 12Z201)
文摘In this paper,a Littlewood-Paley function characterization of the spaces L p（R）,1〈p〈∞,is first established by means of the equivalent conditions of tight wavelet frames,wherein the Littlewood-Paley function is associated with a tight wavelet frame generated by the so-called extension principles.With the above characterization,another characterization of L p（R）,1〈p〈∞,is also established in terms of the weighted l 2-norm of the wavelet frame coefficients,which can be a useful tool in harmonic analysis,approximation theory,and image processing.
