Connections Between the Dirichlet and the Neumann Problem for Continuous and Integrable Boundary Data

2017 ◽  
pp. 85-97 ◽  
Author(s):  
Lucian Beznea ◽  
Mihai N. Pascu ◽  
Nicolae R. Pascu
Keyword(s):  
Neumann Problem ◽  
Boundary Data ◽  
The Neumann Problem

Lp Neumann problem for some Schrödinger equations in (semi-)convex domains

2019 ◽  
Vol 22 (02) ◽  
pp. 1950007
Author(s):  
Sibei Yang ◽  
Dachun Yang
Keyword(s):  
Neumann Problem ◽  
Convex Domain ◽  
Boundary Data ◽  
Muckenhoupt Weight ◽  
Weight Class ◽  
Convex Domains ◽  
Reverse Hölder Class ◽  
Special Cases ◽  
The Neumann Problem ◽  
Reverse Hölder

Let [Formula: see text], [Formula: see text] be a bounded (semi-)convex domain in [Formula: see text] and the non-negative potential [Formula: see text] belong to the reverse Hölder class [Formula: see text]. Assume that [Formula: see text] and [Formula: see text], where [Formula: see text] denotes the Muckenhoupt weight class on [Formula: see text], the boundary of [Formula: see text]. In this paper, the authors show that, for any [Formula: see text], the Neumann problem for the Schrödinger equation [Formula: see text] in [Formula: see text] with boundary data in (weighted) [Formula: see text] is uniquely solvable. The obtained results in this paper essentially improve the known results which are special cases of the results obtained by Shen [Indiana Univ. Math. J. 43 (1994) 143–176] and Tao and Wang [Canad. J. Math. 56 (2004) 655–672], via extending the range [Formula: see text] of [Formula: see text] into [Formula: see text].

scholarly journals The Neumann problem for nonlocal nonlinear diffusion equations

2007 ◽  
Vol 8 (1) ◽  
pp. 189-215 ◽  
Author(s):  
Fuensanta Andreu ◽  
José M. Mazón ◽  
Julio D. Rossi ◽  
Julián Toledo
Keyword(s):  
Neumann Problem ◽  
Nonlinear Diffusion ◽  
Diffusion Equations ◽  
Nonlinear Diffusion Equations ◽  
The Neumann Problem ◽  
Nonlocal Nonlinear
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