scholarly journals Gradient Estimates for Solutions to Divergence Form Elliptic Equations with Discontinuous Coefficients

2000 ◽  
Vol 153 (2) ◽  
pp. 91-151 ◽  
Author(s):  
Yan Yan Li ◽  
Michael Vogelius
Keyword(s):  
Elliptic Equations ◽  
Discontinuous Coefficients ◽  
Divergence Form ◽  
Gradient Estimates

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.

Global gradient estimates for elliptic equations of p(x)-Laplacian type with BMO nonlinearity

2016 ◽  
Vol 2016 (715) ◽  
pp. 1-38 ◽  
Author(s):  
Sun-Sig Byun ◽  
Jihoon Ok ◽  
Seungjin Ryu
Keyword(s):  
Weak Solution ◽  
Elliptic Problem ◽  
Elliptic Equations ◽  
Growth Conditions ◽  
Divergence Form ◽  
Gradient Estimates ◽  
Nonlinear Elliptic Problem ◽  
Nonstandard Growth ◽  
Nonlinear Elliptic ◽  
Nonstandard Growth Conditions

AbstractWe consider a nonlinear elliptic problem in divergence form, with nonstandard growth conditions, on a bounded domain. We obtain the global Calderón–Zygmund type gradient estimates for the weak solution of such a problem in the setting of Lebesgue and Sobolev spaces with variable

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.

Elliptic equations with discontinuous coefficients in generalized Morrey spaces

2017 ◽  
Vol 3 (3) ◽  
pp. 728-762 ◽  
Author(s):  
Giuseppe Di Fazio ◽  
Denny Ivanal Hakim ◽  
Yoshihiro Sawano
Keyword(s):  
Elliptic Equations ◽  
Discontinuous Coefficients ◽  
Morrey Spaces ◽  
Generalized Morrey Spaces
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