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The stability for the Cauchy problem for elliptic equations
We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse
boundary value problems modeled by elliptic equations. We provide essentially optimal …
boundary value problems modeled by elliptic equations. We provide essentially optimal …
Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates
In this article, we review the main results concerning the issue of stability for the
determination of unknown boundary portions of a thermic conducting body from Cauchy …
determination of unknown boundary portions of a thermic conducting body from Cauchy …
Observability inequalities and measurable sets.
This paper presents two observability inequalities for the heat equation over×(0, T). In the
first one, the observation is from a subset of positive measure in×(0, T), while in the second …
first one, the observation is from a subset of positive measure in×(0, T), while in the second …
[PDF][PDF] Optimal stability for inverse elliptic boundary value problems with unknown boundaries
In this paper we study a class of inverse problems associated to elliptic boundary value
problems. More precisely, those inverse problems in which the role of the unknown is played …
problems. More precisely, those inverse problems in which the role of the unknown is played …
The sharp upper bound for the area of the nodal sets of Dirichlet Laplace eigenfunctions
Let Ω Ω be a bounded domain in R^ n R n with C^ 1 C 1 boundary and let u_ λ u λ be a
Dirichlet Laplace eigenfunction in Ω Ω with eigenvalue λ λ. We show that the (n-1)(n-1) …
Dirichlet Laplace eigenfunction in Ω Ω with eigenvalue λ λ. We show that the (n-1)(n-1) …
Unique Continuation at the Boundary for Harmonic Functions in C1 Domains and Lipschitz Domains with Small Constant
Let be a domain, or more generally, a Lipschitz domain with small local Lipschitz constant. In
this paper it is shown that if u is a function harmonic in and continuous in, which vanishes in …
this paper it is shown that if u is a function harmonic in and continuous in, which vanishes in …
Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations
We study local asymptotics of solutions to fractional elliptic equations at boundary points,
under some outer homogeneous Dirichlet boundary condition. Our analysis is based on a …
under some outer homogeneous Dirichlet boundary condition. Our analysis is based on a …
Unique continuation principles for a higher order fractional Laplace equation
In this paper we prove the strong unique continuation principle and the unique continuation
from sets of positive measure for solutions of a higher order fractional Laplace equation in …
from sets of positive measure for solutions of a higher order fractional Laplace equation in …
Boundary Unique Continuation on -Dini Domains and the Size of the Singular Set
Let u be a harmonic function in a C 1-Dini domain D⊂ R d such that u vanishes on a
boundary surface ball∂ D∩ B 5 R (0). We consider an effective version of its singular set …
boundary surface ball∂ D∩ B 5 R (0). We consider an effective version of its singular set …
Examples of non-Dini domains with large singular sets
Let u be a nontrivial harmonic function in a domain D⊂ R d, which vanishes on an open set
of the boundary. In a recent article, we showed that if D is a C 1-Dini domain, then, within the …
of the boundary. In a recent article, we showed that if D is a C 1-Dini domain, then, within the …