scholarly journals A priori bounds inLpfor solutions of elliptic equations in divergence form

2013 ◽  
Vol 137 (7) ◽  
pp. 851-866 ◽  
Author(s):  
Sara Monsurrò ◽  
Maria Transirico
Keyword(s):  
Elliptic Equations ◽  
A Priori ◽  
Divergence Form ◽  
A Priori Bounds

scholarly journals A Priori Bounds in and in for Solutions of Elliptic Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Sara Monsurrò ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
A Priori ◽  
Unbounded Domains ◽  
Variational Problems ◽  
Discontinuous Coefficients ◽  
Elliptic Partial Differential Equations ◽  
Divergence Form ◽  
A Priori Bounds ◽  
A Priori Bound

We give an overview on some recent results concerning the study of the Dirichlet problem for second-order linear elliptic partial differential equations in divergence form and with discontinuous coefficients, in unbounded domains. The main theorem consists in an -a priori bound, . Some applications of this bound in the framework of non-variational problems, in a weighted and a non-weighted case, are also given.

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.

Elliptic equations on manifolds and isoperimetric inequalities

1990 ◽  
Vol 114 (3-4) ◽  
pp. 213-227 ◽  
Author(s):  
Andrea Cianchi
Keyword(s):  
Riemannian Manifolds ◽  
Elliptic Equations ◽  
A Priori ◽  
Neumann Boundary ◽  
Nonlinear Elliptic Equations ◽  
Isoperimetric Inequalities ◽  
Divergence Form ◽  
Sharp Estimates ◽  
Nonlinear Elliptic ◽  
Homogeneous Neumann Boundary Condition

SynopsisWe consider linear and nonlinear elliptic equations in divergence form on Riemannian manifolds with or without boundary. In the former case we impose a homogeneous Neumann boundary condition. By making use of isoperimetric inequalities for manifolds, we obtain a priori sharp estimates for the decreasing rearrangement of the solutions to such equations. These estimates enable us to derive bounds for suitable norms of the solutions and of their gradients.

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.

scholarly journals A priori bounds for superlinear elliptic equations with semidefinite nonlinearity

2017 ◽  
Vol 151 ◽  
pp. 18-40
Author(s):  
Yūki Naito ◽  
Takashi Suzuki ◽  
Yohei Toyota
Keyword(s):  
Elliptic Equations ◽  
A Priori ◽  
A Priori Bounds
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