L p boundary value problems for Schrödinger equations in Lipschitz domain

1998 ◽  
Vol 43 (1) ◽  
pp. 81-82
Author(s):  
Xiangxing Tao
Keyword(s):  
Boundary Value Problems ◽  
Lipschitz Domain ◽  
Boundary Value ◽  
Schrodinger Equations ◽  
Schrödinger Equations

scholarly journals Gradient estimates via rearrangements for solutions of some Schrödinger equations

2018 ◽  
Vol 16 (03) ◽  
pp. 339-361 ◽  
Author(s):  
Sibei Yang ◽  
Der-Chen Chang ◽  
Dachun Yang ◽  
Zunwei Fu
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Gradient Estimates ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Elliptic Boundary Value ◽  
Neumann Boundary Value Problems ◽  
Laplace Type

In this paper, by applying the well-known method for dealing with [Formula: see text]-Laplace type elliptic boundary value problems, the authors establish a sharp estimate for the decreasing rearrangement of the gradient of solutions to the Dirichlet and the Neumann boundary value problems of a class of Schrödinger equations, under the weak regularity assumption on the boundary of domains. As applications, the gradient estimates of these solutions in Lebesgue spaces and Lorentz spaces are obtained.

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