Results 31 to 40 of about 3,278,971 (302)

The Unique Continuation Property of Sublinear Equations [PDF]

SIAM Journal on Mathematical Analysis, 2018
We derive the unique continuation property of a class of semi-linear elliptic equations with non-Lipschitz nonlinearities. The simplest type of equations to which our results apply is given as $-Δu = |u|^{σ-1} u$ in a domain $Ω\subset \mathbb{R}^N$, with $0 \le σ<1$.
Soave, Nicola, Weth, Tobias
openaire   +2 more sources

A frequency function approach to quantitative unique continuation for elliptic equations [PDF]

Journal of Mathematical Analysis and Applications
We investigate the quantitative unique continuation properties of solutions to second-order elliptic equations with lower-order terms. In particular, we establish quantitative forms of the strong unique continuation property for solutions to generalized ...
Blair Davey
semanticscholar   +1 more source

Unique continuation on convex domains

Revista Matemática Iberoamericana, 2022
In this paper, we obtain estimates on the quantitative strata of the critical set of non-trivial harmonic functions u which vanish continuously on V \subset \partial \Omega
openaire   +3 more sources

Unique Continuation for the Kawahara Equation

Trends in Computational and Applied Mathematics, 2007
We establish a unique continuation property for the Kawahara equation. To state such property, we use a Carleman inequality for a linear differential operator related to the Kawahara equation.
P.N. da Silva
doaj   +1 more source

A Carleman inequality on product manifolds and applications to rigidity problems

Advanced Nonlinear Studies, 2023
In this article, we prove a Carleman inequality on a product manifold M×RM\times {\mathbb{R}}. As applications, we prove that (1) a periodic harmonic function on R2{{\mathbb{R}}}^{2} that decays faster than all exponential rate in one direction must be ...
Sun Ao
doaj   +1 more source

On two methods for quantitative unique continuation results for some nonlocal operators [PDF]

Communications in Partial Differential Equations, 2020
In this article, we present two mechanisms for deducing logarithmic quantitative unique continuation bounds for certain classes of integral operators. In our first method, expanding the corresponding integral kernels, we exploit the logarithmic stability
M. A. García‐Ferrero, Angkana Rüland
semanticscholar   +1 more source

Unique continuation from the edge of a crack [PDF]

Mathematics in Engineering, 2020
In this work we develop an Almgren type monotonicity formula for a class of elliptic equations in a domain with a crack, in the presence of potentials satisfying either a negligibility condition with respect to the inverse-square weight or some suitable ...
A. Luca, V. Felli
semanticscholar   +1 more source

Existence, uniqueness and continuity of portfolio choice [PDF]

Zeitschrift für Nationalökonomie, 1974
A complete version of this paper, which includes all proofs, may be obtained on request from the second author.
Davies, Laurie, Ronning, Gerd
openaire   +2 more sources

Unique continuation property for biharmonic hypersurfaces in spheres [PDF]

Annals of Global Analysis and Geometry, 2020
We prove a unique continuation theorem for non-minimal biharmonic hypersurfaces of spheres, based on Aronszajn’s 1957 article. Under the right hypotheses, this result shows that, for these immersions, CMC on an open subset implies globally CMC.
Hiba Bibi, E. Loubeau, C. Oniciuc
semanticscholar   +1 more source

Strong unique continuation for the higher order fractional Laplacian [PDF]

Mathematics in Engineering, 2019
In this article we study the strong unique continuation property for solutions of higher order (variable coefficient) fractional Schr\"odinger operators.
M. Garc'ia-Ferrero, Angkana Ruland
semanticscholar   +1 more source