We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across th...We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.展开更多
Let A be a symmetric and positive definite(1,1)tensor on a bounded domain Ω in an ndimensional metric measure space(R^n,<,>,e^-φdv).In this paper,we investigate the Dirichlet eigenvalue problem of a system of ...Let A be a symmetric and positive definite(1,1)tensor on a bounded domain Ω in an ndimensional metric measure space(R^n,<,>,e^-φdv).In this paper,we investigate the Dirichlet eigenvalue problem of a system of equations of elliptic operators in weighted divergence form{LA,φu+α▽(divu)-▽φdivu]=-su,inΩ,u∣aΩ=0,where LA,φ=div(A▽(·))-(A▽φ,▽(·)),α is a nonnegative constant and u is a vector-valued function.Some universal inequalities for eigenvalues of this problem are established.Moreover,as applications of these results,we give some estimates for the upper bound of sk+1 and the gap of sk+1-sk in terms of the first k eigenvalues.Our results contain some results for the Lam′e system and a system of equations of the drifting Laplacian.展开更多
In this paper, we study the existence and nonuniqueness of weak solutions of the initial and boundary value problem for ut= uσdiv(|△u|p-2△u) with σ≥1. Localization property of weak solutions is also discussed.
In this paper, we prove the existence and nonuniqueness of the weak solutions of the initial and boundary value problem for a nonlinear degenerate parabolic equation not in divergence form. Localization property of we...In this paper, we prove the existence and nonuniqueness of the weak solutions of the initial and boundary value problem for a nonlinear degenerate parabolic equation not in divergence form. Localization property of weak solutions will be also discussed.展开更多
We establish conditions of the nonexistence of weak solutions of the Dirich- let problem for nonlinear elliptic equations of arbitrary even order with some right- hand sides from Lm where m ~ 1. The conditions include...We establish conditions of the nonexistence of weak solutions of the Dirich- let problem for nonlinear elliptic equations of arbitrary even order with some right- hand sides from Lm where m ~ 1. The conditions include the requirement of a certain closeness of the parameter m to 1.展开更多
基金supported by National Natural Science Foundation of China(12061080,12161087 and 12261093)the Science and Technology Project of the Education Department of Jiangxi Province(GJJ211601)supported by National Natural Science Foundation of China(11871305).
文摘We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.
基金supported by the National Natural Science Foundation of China(Grant Nos.1100113011571361 and 11831005)the Fundamental Research Funds for the Central Universities(Grant No.30917011335)。
文摘Let A be a symmetric and positive definite(1,1)tensor on a bounded domain Ω in an ndimensional metric measure space(R^n,<,>,e^-φdv).In this paper,we investigate the Dirichlet eigenvalue problem of a system of equations of elliptic operators in weighted divergence form{LA,φu+α▽(divu)-▽φdivu]=-su,inΩ,u∣aΩ=0,where LA,φ=div(A▽(·))-(A▽φ,▽(·)),α is a nonnegative constant and u is a vector-valued function.Some universal inequalities for eigenvalues of this problem are established.Moreover,as applications of these results,we give some estimates for the upper bound of sk+1 and the gap of sk+1-sk in terms of the first k eigenvalues.Our results contain some results for the Lam′e system and a system of equations of the drifting Laplacian.
基金The Young Teachers Foundation (420010302318) of Jilin University.
文摘In this paper, we study the existence and nonuniqueness of weak solutions of the initial and boundary value problem for ut= uσdiv(|△u|p-2△u) with σ≥1. Localization property of weak solutions is also discussed.
文摘In this paper, we prove the existence and nonuniqueness of the weak solutions of the initial and boundary value problem for a nonlinear degenerate parabolic equation not in divergence form. Localization property of weak solutions will be also discussed.
文摘We establish conditions of the nonexistence of weak solutions of the Dirich- let problem for nonlinear elliptic equations of arbitrary even order with some right- hand sides from Lm where m ~ 1. The conditions include the requirement of a certain closeness of the parameter m to 1.
