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 ◽  
Keyword(s):  
Weak Solutions ◽  
Elliptic Equations ◽  
A Priori ◽  
A Priori Bounds ◽  
Nonstandard Growth

scholarly journals A-priori bounds and existence for solutions of weighted elliptic equations with a convection term

2017 ◽  
Vol 6 (4) ◽  
pp. 427-445 ◽  
Author(s):  
Ky Ho ◽  
Inbo Sim
Keyword(s):  
Elliptic Equations ◽  
Neumann Boundary Condition ◽  
Existence Of Solutions ◽  
A Priori ◽  
Neumann Boundary ◽  
Variable Exponents ◽  
Convection Term ◽  
Pseudomonotone Operators ◽  
A Priori Bounds ◽  
Localization Method

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.

scholarly journals AnLp-Estimate for Weak Solutions of Elliptic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Sara Monsurrò ◽  
Maria Transirico
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
A Priori ◽  
Unbounded Domains ◽  
Discontinuous Coefficients ◽  
Elliptic Partial Differential Equations ◽  
Divergence Form ◽  
A Priori Bound

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.

Schauder estimates and existence theory for entire solutions of linear elliptic equations

1988 ◽  
Vol 110 (1-2) ◽  
pp. 101-123 ◽  
Author(s):  
Heinrich Begehr ◽  
G.N. Hile
Keyword(s):  
Weak Solutions ◽  
Elliptic Equations ◽  
Dimensional Space ◽  
A Priori ◽  
Growth Conditions ◽  
Existence Theory ◽  
Uniqueness Theorems ◽  
Entire Solutions ◽  
Schauder Estimates

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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