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.

Some uniqueness results for singular elliptic problems

2015 ◽  
Vol 26 (03) ◽  
pp. 1550026 ◽  
Author(s):  
L. Caso ◽  
R. D'Ambrosio
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Sobolev Spaces ◽  
Open Subset ◽  
Weighted Sobolev Spaces ◽  
Elliptic Partial Differential Equations ◽  
Divergence Form ◽  
Dirichlet Problems ◽  
Uniqueness Results ◽  
Singular Data

We prove some uniqueness results for Dirichlet problems for second-order linear elliptic partial differential equations in non-divergence form with singular data in suitable weighted Sobolev spaces, on an open subset Ω of ℝn, n ≥ 2, not necessarily bounded or regular.

On the Dirichlet problem for weakly non-linear elliptic partial differential equations

1977 ◽  
Vol 76 (4) ◽  
pp. 283-300 ◽  
Author(s):  
E. N. Dancer
Keyword(s):  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Weakly Nonlinear ◽  
Partial Derivatives ◽  
Nonlinear Elliptic ◽  
Non Linear

SynopsisWe study the existence of solutions of the Dirichlet problem for weakly nonlinear elliptic partial differential equations. We only consider cases where the nonlinearities do not depend on any partial derivatives. For these cases, we prove the existence of solutions for a wide variety of nonlinearities.

scholarly journals On the Cauchy problem for semilinear elliptic equations

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Nguyen Huy Tuan ◽  
Tran Thanh Binh ◽  
Tran Quoc Viet ◽  
Daniel Lesnic
Keyword(s):  
Cauchy Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Hilbert Spaces ◽  
Elliptic Equations ◽  
Elliptic Partial Differential Equations ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
The Cauchy Problem ◽  
Ill Posed

AbstractWe study the Cauchy problem for nonlinear (semilinear) elliptic partial differential equations in Hilbert spaces. The problem is severely ill-posed in the sense of Hadamard. Under a weak

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.

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