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学者姓名：王立河
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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 Intrinsic scaling Vitali covering
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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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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 ：
directional homogenization elliptic systems in divergence form Regularity
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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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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 Maximal function Vitali covering
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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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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 ：
BMO space Composite Reifenberg domain Fourth order elliptic system Global W-2,W-P estimate
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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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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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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 ：
L-p estimates Maximal function Stokes equations Vitali covering lemma
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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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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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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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Abstract ：
This study proposes a pricing model through allowing for stochastic interest rate and stochastic volatility in the double exponential jump-diffusion setting. The characteristic function of the proposed model is then derived. Fast numerical solutions for European call and put options pricing based on characteristic function and fast Fourier transform (FFT) technique are developed. Simulations show that our numerical technique is accurate, fast and easy to implement, the proposed model is suitable for modeling long-time real-market changes. The model and the proposed option pricing method are useful for empirical analysis of asset returns and risk management in firms. (C) 2012 Elsevier B. V. All rights reserved.
Keyword ：
Characteristic function Double exponential jump diffusion Fast Fourier transform Stochastic interest rate Stochastic volatility
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| GB/T 7714 | Zhang, Sumei , Wang, Lihe . A fast numerical approach to option pricing with stochastic interest rate, stochastic volatility and double jumps [J]. | COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION , 2013 , 18 (7) : 1832-1839 . |
| MLA | Zhang, Sumei 等. "A fast numerical approach to option pricing with stochastic interest rate, stochastic volatility and double jumps" . | COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 18 . 7 (2013) : 1832-1839 . |
| APA | Zhang, Sumei , Wang, Lihe . A fast numerical approach to option pricing with stochastic interest rate, stochastic volatility and double jumps . | COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION , 2013 , 18 (7) , 1832-1839 . |
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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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