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Daniele Tampieri
Daniele Tampieri
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What is the the method"method of ascendingascending" in the study of elliptic systems in dimension two?

I have read a paper named "CONVERGENCE RATES AND HÖLDER ESTIMATES IN ALMOST-PERIODIC HOMOGENIZATION OF ELLIPTIC SYSTEMS"of Z. Shen [1]. In the paper the autherauthor mentioned we can deal with thetwo-dimensional elliptic systems with two dimensions by adding a dummy variable (the method of ascending) and use the results of dimensionon the related three-dimensional problem. I guess it is a standard statementsway to deal with the elliptic systems with lower dimensions. However, I do not find any reference about it,: can you give me some references or hints?

Reference

[1] Zhongwei Shen, "Convergence rates and Hölder estimates in almost-periodic homogenization of elliptic systems" (English), Analysis & PDE 8, No. 7, 1565-1601 (2015), DOI: 10.2140/apde.2015.8.1541, MR3399132, Zbl 1327.35025.

What is the the method of ascending in study of elliptic systems in dimension two?

I have read a paper named "CONVERGENCE RATES AND HÖLDER ESTIMATES IN ALMOST-PERIODIC HOMOGENIZATION OF ELLIPTIC SYSTEMS". In the paper the auther mentioned we can deal with the elliptic systems with two dimensions by adding a dummy variable (the method of ascending) and use the results of dimension three. I guess it is a standard statements to deal with the elliptic systems with lower dimensions. However, I do not find any reference about it, can you give me some references or hints?

What is the the "method of ascending" in the study of elliptic systems in dimension two?

I have read a paper of Z. Shen [1]. In the paper the author mentioned we can deal with two-dimensional elliptic systems by adding a dummy variable (the method of ascending) and use the results on the related three-dimensional problem. I guess it is a standard way to deal with elliptic systems with lower dimensions. However, I do not find any reference about it: can you give me some references or hints?

Reference

[1] Zhongwei Shen, "Convergence rates and Hölder estimates in almost-periodic homogenization of elliptic systems" (English), Analysis & PDE 8, No. 7, 1565-1601 (2015), DOI: 10.2140/apde.2015.8.1541, MR3399132, Zbl 1327.35025.

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Luis Yanka Annalisc
Luis Yanka Annalisc
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What is the the method of ascending in study of elliptic systems in dimension two?

I have read a paper named "CONVERGENCE RATES AND HÖLDER ESTIMATES IN ALMOST-PERIODIC HOMOGENIZATION OF ELLIPTIC SYSTEMS". In the paper the auther mentioned we can deal with the elliptic systems with two dimensions by adding a dummy variable (the method of ascending) and use the results of dimension three. I guess it is a standard statements to deal with the elliptic systems with lower dimensions. However, I do not find any reference about it, can you give me some references or hints?