scholarly journals Elliptic equations with nonzero boundary conditions in weighted Sobolev spaces

2008 ◽  
Vol 337 (2) ◽  
pp. 1465-1479 ◽  
Author(s):  
Doyoon Kim
Keyword(s):  
Boundary Conditions ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Weighted Sobolev Spaces ◽  
Nonzero Boundary

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 W2,p-Solvability of the Dirichlet Problem for Elliptic Equations with Singular Data

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Loredana Caso ◽  
Roberta D’Ambrosio ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Sobolev Spaces ◽  
Unique Solvability ◽  
Elliptic Equations ◽  
Weighted Sobolev Spaces ◽  
Elliptic Partial Differential Equations ◽  
Planar Case ◽  
Singular Data

We give an overview on some results concerning the unique solvability of the Dirichlet problem inW2,p,p>1, for second-order linear elliptic partial differential equations in nondivergence form and with singular data in weighted Sobolev spaces. We also extend such results to the planar case.

Elliptic equations in weighted Sobolev spaces of infinite order with L 1 data

2009 ◽  
Vol 33 (1) ◽  
pp. 49-56 ◽  
Author(s):  
Mostafa Bendahmane ◽  
Moussa Chrif ◽  
Said El Manouni
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Infinite Order ◽  
Weighted Sobolev Spaces

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.

scholarly journals Existence and uniqueness of solutions for a class of degenerate nonlinear elliptic equations

2016 ◽  
Vol 70 (2) ◽  
pp. 9
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Spaces ◽  
Nonlinear Elliptic Equations ◽  
Uniqueness Of Solutions ◽  
Nonlinear Elliptic

In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations \begin{align} {\Delta}(v(x)\, {\vert{\Delta}u\vert}^{p-2}{\Delta}u) &-\sum_{j=1}^n D_j{\bigl[}{\omega}_1(x) \mathcal{A}_j(x, u, {\nabla}u){\bigr]}+ b(x,u,{\nabla}u)\, {\omega}_2(x)\\ & = f_0(x) - \sum_{j=1}^nD_jf_j(x), \ \ {\rm in } \ \ {\Omega} \end{align} in the setting of the weighted Sobolev spaces.

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