The Douglas formula in Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}

被引：0
作者：
Krzysztof Bogdan
Damian Fafuła
Artur Rutkowski
机构：
[1] Wrocław University of Science and Technology,Faculty of Pure and Applied Mathematics
[2] Norwegian University of Science and Technology,undefined
来源：
Nonlinear Differential Equations and Applications NoDEA | 2023年 / 30卷 / 4期
关键词：
Douglas formula; Laplacian; Harmonic function; Trace theorem; Primary 46E35; Secondary 31B25; 35A15;
D O I：
10.1007/s00030-023-00865-9
中图分类号：
学科分类号：
摘要：
We prove a Douglas-type identity in Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document} for 1<p<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1<p<\infty $$\end{document}.
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[1]  
Aikawa H(2007)Boundary Harnack principle for Potential Anal. 26 281-301
[2]  
Kilpeläinen T(1979)-harmonic functions in smooth Euclidean domains Rend. Sem. Mat. Univ. Padova 60 1978-337
[3]  
Shanmugalingam N(2000)BV functions and traces J. Math. Anal. Appl. 243 326-215
[4]  
Zhong X(2014)Sharp estimates for the Green function in Lipschitz domains Hiroshima Math. J. 44 193-67
[5]  
Anzellotti G(2018)On Hardy spaces of local and nonlocal operators Topol. Methods Nonlinear Anal. 52 49-288
[6]  
Giaquinta M(1977)On certain variant of strongly nonlinear multidimensional interpolation inequality Arch. Ration. Mech. Anal. 65 275-458
[7]  
Bogdan K(1957)Estimates of harmonic measure Bull. Soc. Math. France 85 431-621
[8]  
Bogdan K(1962)Conditional Brownian motion and the boundary limits of harmonic functions Ann. Inst. Fourier 12 573-321
[9]  
Dyda B(1931)Boundary properties of functions with finite Dirichlet integrals Trans. Am. Math. Soc. 33 263-46
[10]  
Luks T(1982)Solution of the problem of Plateau Acta Math. 148 31-521
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