scholarly journals Elliptic Equations with Discontinuous Coefficients in Weighted Sobolev Spaces on Unbounded Domains

2001 ◽  
Vol 253 (1) ◽  
pp. 297-309 ◽  
Author(s):  
Patrizia Di Gironimo ◽  
Antonio Vitolo
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Discontinuous Coefficients

scholarly journals Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Serena Boccia ◽  
Sara Monsurrò ◽  
Maria Transirico
Keyword(s):  
Uniqueness Theorem ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
A Priori ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Regularity Result ◽  
Second Order ◽  
Order Linear ◽  
A Priori Bound

We study in this paper a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of , . We obtain an a priori bound, and a regularity result from which we deduce a uniqueness theorem.

scholarly journals Uniqueness Results for Higher Order Elliptic Equations in Weighted Sobolev Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Loredana Caso ◽  
Patrizia Di Gironimo ◽  
Sara Monsurrò ◽  
Maria Transirico
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Weighted Sobolev Spaces ◽  
Discontinuous Coefficients ◽  
Uniqueness Results ◽  
Elliptic Differential Equations

We prove some uniqueness results for the solution of two kinds of Dirichlet boundary value problems for second- and fourth-order linear elliptic differential equations with discontinuous coefficients in polyhedral angles, in weighted Sobolev spaces.

The Dirichlet problem for elliptic equations in weighted Sobolev spaces on unbounded domains of the plane

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Serena Boccia ◽  
Maria Salvato ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
A Priori ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Uniqueness Result ◽  
Order Linear ◽  
A Priori Bound

AbstractThis paper deals with the Dirichlet problem for second order linear elliptic equations in unbounded domains of the plane in weighted Sobolev spaces. We prove an a priori bound and an existence and uniqueness result.

Semilinear elliptic equations in unbounded domains of Rn

1981 ◽  
Vol 88 (1-2) ◽  
pp. 109-119 ◽  
Author(s):  
Patrizia Donato ◽  
Lucia Migliaccio ◽  
Rosanna Schianchi
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Nonlinear Term ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Quadratic Growth ◽  
Multiplicity Results ◽  
Semilinear Elliptic ◽  
Least Solution ◽  
Semilinear Problem

SynopsisWe study, in unbounded domains Ω⊂Rn, an elliptic semilinear problem with homogeneous boundary conditions. We assume that the nonlinear term f(x, u, Du) satisfies some condition of quadratic growth with respect to Du. We prove, in the framework of weighted Sobolev spaces, that, if and are respectively a subsolution and a supersolution of our problem, then there exists a least solution ū and a greatest solution û in the ordered interval and we obtain some multiplicity results.

scholarly journals Multiple solutions for some strongly degenerate second order elliptic equations

2021 ◽  
pp. 1-12
Author(s):  
João R. Santos ◽  
Gaetano Siciliano
Keyword(s):  
Boundary Value Problem ◽  
Bounded Domain ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Existence Of Solutions ◽  
Weighted Sobolev Spaces ◽  
Degenerate Operator ◽  
Second Order Elliptic Equations ◽  
Strongly Degenerate

We consider a boundary value problem in a bounded domain involving a degenerate operator of the form L ( u ) = − div ( a ( x ) ∇ u ) and a suitable nonlinearity f. The function a vanishes on smooth 1-codimensional submanifolds of Ω where it is not allowed to be C 2 . By using weighted Sobolev spaces we are still able to find existence of solutions which vanish, in the trace sense, on the set where a vanishes.

scholarly journals On Entropy Solutions of Anisotropic Elliptic Equations with Variable Nonlinearity Indices

2017 ◽  
Vol 63 (3) ◽  
pp. 475-493 ◽  
Author(s):  
L M Kozhevnikova
Keyword(s):  
Dirichlet Problem ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Unbounded Domains ◽  
Second Order ◽  
Entropy Solutions ◽  
Anisotropic Sobolev Spaces ◽  
Right Hand ◽  
Anisotropic Elliptic Equations

For a certain class of second-order anisotropic elliptic equations with variable nonlinearity indices and L1 right-hand side we consider the Dirichlet problem in arbitrary unbounded domains. We prove the existence and uniqueness of entropy solutions in anisotropic Sobolev spaces with variable indices.

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