scholarly journals A priori bounds for weak solutions to elliptic equations with nonstandard growth

2012 ◽  
Vol 5 (4) ◽  
pp. 865-878 ◽  
Author(s):  
Patrick Winkert ◽  
◽  
Rico Zacher ◽  
2017 ◽  
Vol 6 (4) ◽  
pp. 427-445 ◽  
Author(s):  
Ky Ho ◽  
Inbo Sim

AbstractWe investigate weighted elliptic equations containing a convection term with variable exponents that are subject to Dirichlet or Neumann boundary condition. By employing the De Giorgi iteration and a localization method, we give a-priori bounds for solutions to these problems. The existence of solutions is also established using Brezis’ theorem for pseudomonotone operators.


2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Sara Monsurrò ◽  
Maria Transirico

We prove anLp-a priori bound,p>2, for solutions of second order linear elliptic partial differential equations in divergence form with discontinuous coefficients in unbounded domains.


1988 ◽  
Vol 110 (1-2) ◽  
pp. 101-123 ◽  
Author(s):  
Heinrich Begehr ◽  
G.N. Hile

SynopsisExistence as well as uniqueness theorems under certain growth conditions are given for entire solutions to linear elliptic equations in the n-dimensional space (2≦n). Introducing a proper norm, the proofs are based on a priori estimates. These estimates could be used to solve nonlinear equationsin the space, but the conditions on the nonlinearity have to be strong as the a priori estimates applyonly to classical, not to weak, solutions.


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