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学者姓名:王立河

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Global regularity of parabolic p-Laplace equations on convex domains EI SCIE Scopus
期刊论文 | 2018 , 169 , 118-129 | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
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Abstract :

We show the global regularity of the nonhomogeneous parabolic p-Laplace equations on convex domains. Starting with the local up-to-boundary Lipschitz regularity for the homogeneous equation, we derive the global a priori estimates via Vitali covering coupling with p-harmonic approximation. Moreover, the exponents in the a priori estimates come from the intrinsic scaling. (C) 2017 Elsevier Ltd. All rights reserved.

Keyword :

Barrier function Vitali covering Intrinsic scaling

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GB/T 7714 Jia, Huilian , Wang, Lihe . Global regularity of parabolic p-Laplace equations on convex domains [J]. | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS , 2018 , 169 : 118-129 .
MLA Jia, Huilian 等. "Global regularity of parabolic p-Laplace equations on convex domains" . | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 169 (2018) : 118-129 .
APA Jia, Huilian , Wang, Lihe . Global regularity of parabolic p-Laplace equations on convex domains . | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS , 2018 , 169 , 118-129 .
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REGULARITY OF ELLIPTIC SYSTEMS IN DIVERGENCE FORM WITH DIRECTIONAL HOMOGENIZATION SCIE Scopus
期刊论文 | 2018 , 38 (1) , 75-90 | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
WoS CC Cited Count: 1 SCOPUS Cited Count: 1
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Abstract :

In this paper, we study regularity of solutions of elliptic systems in divergence form with directional homogenization. Here directional homogenization means that the coefficients of equations are rapidly oscillating only in some directions. We will investigate the different regularity of solutions on directions with homogenization and without homogenization. Actually, we obtain uniform interior W-1,W-p estimates in all directions and uniform interior C-1,C-gamma estimatesin the directions without homogenization.

Keyword :

Regularity elliptic systems in divergence form directional homogenization

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GB/T 7714 Dong, Rong , Li, Dongsheng , Wang, Lihe . REGULARITY OF ELLIPTIC SYSTEMS IN DIVERGENCE FORM WITH DIRECTIONAL HOMOGENIZATION [J]. | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS , 2018 , 38 (1) : 75-90 .
MLA Dong, Rong 等. "REGULARITY OF ELLIPTIC SYSTEMS IN DIVERGENCE FORM WITH DIRECTIONAL HOMOGENIZATION" . | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 38 . 1 (2018) : 75-90 .
APA Dong, Rong , Li, Dongsheng , Wang, Lihe . REGULARITY OF ELLIPTIC SYSTEMS IN DIVERGENCE FORM WITH DIRECTIONAL HOMOGENIZATION . | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS , 2018 , 38 (1) , 75-90 .
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Quasilinear elliptic equations on convex domains SCIE Scopus
期刊论文 | 2016 , 433 (1) , 509-524 | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | IF: 1.064
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Abstract :

We show global regularity for p-Laplacian type elliptic equations on convex domains with W-1,W-q(q >= p > 1) boundary data. The maximal function, Vitali covering lemma and approximation (or compactness method) are the main techniques in the proof. To derive the approximation lemma, we need W-1,W-infinity estimates for the corresponding homogeneous equations, where the convexity of the domain plays an important role. (C) 2015 Elsevier Inc. All rights reserved.

Keyword :

Compactness method Vitali covering Maximal function

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GB/T 7714 Jia, Huilian , Wang, Lihe . Quasilinear elliptic equations on convex domains [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2016 , 433 (1) : 509-524 .
MLA Jia, Huilian 等. "Quasilinear elliptic equations on convex domains" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 433 . 1 (2016) : 509-524 .
APA Jia, Huilian , Wang, Lihe . Quasilinear elliptic equations on convex domains . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2016 , 433 (1) , 509-524 .
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Hessian estimates for fourth order elliptic systems with singular BMO coefficients in composite Reifenberg domains SCIE Scopus
期刊论文 | 2015 , 268 (3) , 555-584 | JOURNAL OF FUNCTIONAL ANALYSIS | IF: 1.273
WoS CC Cited Count: 5 SCOPUS Cited Count: 5
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Abstract :

We consider fourth order elliptic systems in divergence form with greatly discontinuous coefficients in a nonsmooth domain. Our domain is composed of a finite number of disjoint subdomains with (delta, R)-Reifenberg flat boundaries, and the coefficients, which are allowed to have great discontinuity across the boundaries of subdomains, have small BMO seminorms on each subdomain. Our main result is deriving the global W-2,W-p (1 <p < infinity) regularity, with the estimates independent of the distance between the subdomains. (C) 2014 Elsevier Inc. All rights reserved.

Keyword :

Global W-2,W-P estimate Fourth order elliptic system Composite Reifenberg domain BMO space

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GB/T 7714 Hu, Fangju , Li, Dongsheng , Wang, Lihe . Hessian estimates for fourth order elliptic systems with singular BMO coefficients in composite Reifenberg domains [J]. | JOURNAL OF FUNCTIONAL ANALYSIS , 2015 , 268 (3) : 555-584 .
MLA Hu, Fangju 等. "Hessian estimates for fourth order elliptic systems with singular BMO coefficients in composite Reifenberg domains" . | JOURNAL OF FUNCTIONAL ANALYSIS 268 . 3 (2015) : 555-584 .
APA Hu, Fangju , Li, Dongsheng , Wang, Lihe . Hessian estimates for fourth order elliptic systems with singular BMO coefficients in composite Reifenberg domains . | JOURNAL OF FUNCTIONAL ANALYSIS , 2015 , 268 (3) , 555-584 .
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A new proof of L-p estimates of Stokes equations SCIE Scopus
期刊论文 | 2014 , 420 (2) , 1251-1264 | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | IF: 1.12
WoS CC Cited Count: 1 SCOPUS Cited Count: 1
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Abstract :

In this paper, we establish a new proof of L-p estimates of the Stokes equations, which enables us to avoid the use of potential theory and thus simplifies the traditional proof. The modified Vitali covering lemma and the maximal function technique are the main analytical tools. (C) 2014 Elsevier Inc. All rights reserved.

Keyword :

Vitali covering lemma Maximal function Stokes equations L-p estimates

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GB/T 7714 Hu, Fangju , Li, Dongsheng , Wang, Lihe . A new proof of L-p estimates of Stokes equations [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2014 , 420 (2) : 1251-1264 .
MLA Hu, Fangju 等. "A new proof of L-p estimates of Stokes equations" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 420 . 2 (2014) : 1251-1264 .
APA Hu, Fangju , Li, Dongsheng , Wang, Lihe . A new proof of L-p estimates of Stokes equations . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2014 , 420 (2) , 1251-1264 .
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Boundary behavior of solutions of elliptic equations in nondivergence form SCIE Scopus
期刊论文 | 2014 , 143 (3-4) , 525-541 | MANUSCRIPTA MATHEMATICA | IF: 0.519
WoS CC Cited Count: 2 SCOPUS Cited Count: 3
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Abstract :

A new proof for boundary Lipschitz estimate is shown for solutions of elliptic equations in nondivergence form. Under additional condition, the boundary differentiability is obtained.

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GB/T 7714 Huang, Yongpan , Li, Dongsheng , Wang, Lihe . Boundary behavior of solutions of elliptic equations in nondivergence form [J]. | MANUSCRIPTA MATHEMATICA , 2014 , 143 (3-4) : 525-541 .
MLA Huang, Yongpan 等. "Boundary behavior of solutions of elliptic equations in nondivergence form" . | MANUSCRIPTA MATHEMATICA 143 . 3-4 (2014) : 525-541 .
APA Huang, Yongpan , Li, Dongsheng , Wang, Lihe . Boundary behavior of solutions of elliptic equations in nondivergence form . | MANUSCRIPTA MATHEMATICA , 2014 , 143 (3-4) , 525-541 .
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Lateral boundary differentiability of solutions of parabolic equations on cylindrical convex domains SCIE Scopus
期刊论文 | 2013 , 404 (1) , 36-46 | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | IF: 1.119
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Abstract :

The lateral boundary differentiability with respect to x is shown for solutions of parabolic differential equations in nondivergence form on cylindrical convex domains. (C) 2013 Elsevier Inc. All rights reserved.

Keyword :

Cylindrical convex domains Lateral boundary differentiability Parabolic equations

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GB/T 7714 Huang, Yongpan , Li, Dongsheng , Wang, Lihe . Lateral boundary differentiability of solutions of parabolic equations on cylindrical convex domains [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2013 , 404 (1) : 36-46 .
MLA Huang, Yongpan 等. "Lateral boundary differentiability of solutions of parabolic equations on cylindrical convex domains" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 404 . 1 (2013) : 36-46 .
APA Huang, Yongpan , Li, Dongsheng , Wang, Lihe . Lateral boundary differentiability of solutions of parabolic equations on cylindrical convex domains . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2013 , 404 (1) , 36-46 .
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Lateral boundary differentiability of solutions of parabolic equations in nondivergence form SCIE Scopus
期刊论文 | 2013 , 255 (10) , 3491-3504 | JOURNAL OF DIFFERENTIAL EQUATIONS | IF: 1.57
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Abstract :

The lateral boundary differentiability is shown for solutions of parabolic differential equations in nondivergence form under the assumptions that the parabolic boundary satisfies the exterior Dini condition and is punctually C-1 differentiable one-sided in t-direction. The classical barrier technique, the maximum principle, the interior Harnack inequality and an iteration procedure are the main analytical tools. (C) 2013 Elsevier Inc. All rights reserved.

Keyword :

Lateral boundary differentiability Parabolic equations

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GB/T 7714 Huang, Yongpan , Li, Dongsheng , Wang, Lihe . Lateral boundary differentiability of solutions of parabolic equations in nondivergence form [J]. | JOURNAL OF DIFFERENTIAL EQUATIONS , 2013 , 255 (10) : 3491-3504 .
MLA Huang, Yongpan 等. "Lateral boundary differentiability of solutions of parabolic equations in nondivergence form" . | JOURNAL OF DIFFERENTIAL EQUATIONS 255 . 10 (2013) : 3491-3504 .
APA Huang, Yongpan , Li, Dongsheng , Wang, Lihe . Lateral boundary differentiability of solutions of parabolic equations in nondivergence form . | JOURNAL OF DIFFERENTIAL EQUATIONS , 2013 , 255 (10) , 3491-3504 .
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HOLDER ESTIMATES FOR A CLASS OF DEGENERATE ELLIPTIC EQUATIONS SCIE Scopus CSCD
期刊论文 | 2013 , 33 (4) , 1202-1218 | ACTA MATHEMATICA SCIENTIA | IF: 0.62
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Abstract :

In this paper we study the regularity theory of the solutions of a class of degenerate elliptic equations in divergence form. By introducing a proper distance and applying the compactness method we establish the Holder type estimates for the weak solutions.

Keyword :

compactness method degenerate elliptic equations Holder estimates

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GB/T 7714 Song, Qiaozhen , Wang, Lihe , Li, Dongsheng . HOLDER ESTIMATES FOR A CLASS OF DEGENERATE ELLIPTIC EQUATIONS [J]. | ACTA MATHEMATICA SCIENTIA , 2013 , 33 (4) : 1202-1218 .
MLA Song, Qiaozhen 等. "HOLDER ESTIMATES FOR A CLASS OF DEGENERATE ELLIPTIC EQUATIONS" . | ACTA MATHEMATICA SCIENTIA 33 . 4 (2013) : 1202-1218 .
APA Song, Qiaozhen , Wang, Lihe , Li, Dongsheng . HOLDER ESTIMATES FOR A CLASS OF DEGENERATE ELLIPTIC EQUATIONS . | ACTA MATHEMATICA SCIENTIA , 2013 , 33 (4) , 1202-1218 .
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A symmetry result for the torsion equation in an unbounded domain in 2D SCIE Scopus
期刊论文 | 2013 , 407 (2) , 550-556 | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | IF: 1.119
WoS CC Cited Count: 1 SCOPUS Cited Count: 1
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Abstract :

We investigate an overdetermined problem for the torsion equation Delta u = -1 with two kinds of free boundary conditions in an unbounded domain and present a symmetry result in the case of 2D. The proof is based on the maximum principle. In the proof, we use the sliding method and some convex arguments. (C) 2013 Elsevier Inc. All rights reserved.

Keyword :

Unbounded domain Maximum principle Overdetermined problem Symmetry

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GB/T 7714 Wang, Lihe , Wang, Lizhou . A symmetry result for the torsion equation in an unbounded domain in 2D [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2013 , 407 (2) : 550-556 .
MLA Wang, Lihe 等. "A symmetry result for the torsion equation in an unbounded domain in 2D" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 407 . 2 (2013) : 550-556 .
APA Wang, Lihe , Wang, Lizhou . A symmetry result for the torsion equation in an unbounded domain in 2D . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2013 , 407 (2) , 550-556 .
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