Corpus ID: 152282270

Fefferman's Inequality and Unique Continuation Property of Elliptic Partial Differential Equations

@article{Tumalun2019FeffermansIA,
  title={Fefferman's Inequality and Unique Continuation Property of Elliptic Partial Differential Equations},
  author={N. K. Tumalun and D. Hakim and H. Gunawan},
  journal={arXiv: Analysis of PDEs},
  year={2019}
}
In this paper we prove a Fefferman's inequality for potentials belonging to a generalized Morrey space $ L^{p,\varphi} $ and a Stummel class $ \tilde{S}_{\alpha,p} $. Our result extends the previous Fefferman's inequality that was obtained in \cite{CF,F} for the case of Morrey spaces, and that in \cite{Z1} for the case of Stummel classes, which was restated recently in \cite{CRR}. Using this inequality, we prove a strong unique continuation property of a second order elliptic partial… Expand

References

SHOWING 1-10 OF 26 REFERENCES
A Remark on a Paper by C. Fefferman
We give a simplified proof of an imbedding theorem by C. Fefferman [3]. The purpose of this paper is to provide a simplified proof of a deep result by C. Fefferman (see [3,1]) concerning theExpand
On the solutions of quasi-linear elliptic partial differential equations
The literature concerning these equations being very extensive, we shall not attempt to give a complete list of references. The starting point for many more modern researches has been the work of S.Expand
A note on the Kato class and some applications
In a self contained presentation we study some properties of the class $$\widetilde{K}_n$$K~n which is a slight variant of the usual Kato class $$K_n$$Kn. As application we show the strong uniqueExpand
Generalized Morrey Spaces for Non-doubling Measures
Abstract.In this paper, we define the generalized Morrey spaces on $${\mathbb{R}}^{d}$$ with the measure μ non-doubling. After defining the space, we shall investigate the properties of maximalExpand
On certain convolution inequalities
It is proved that certain convolution inequalities are easy consequences of the Hardy-Littlewood-Wiener maximal theorem. These inequalities include the Hardy-Littlewood-Sobolev inequality forExpand
Inclusion between generalized Stummel classes and other function spaces
We refine the definition of generalized Stummel classes and study inclusion properties of these classes. We also study the inclusion relation between Stummel classes and other function spaces such asExpand
A Potential Theoretic Inequality
In this paper is proved a weighted inequality for Riesz potential similar to the classical one by D. Adams. Here the gain of integrability is not always algebraic, as in the classical case, butExpand
Partial Differential Equations
THE appearance of these volumes marks the happy conclusion of a work undertaken, as the author reminds us in his preface, twenty-one years ago. Doubtless it would have been finished earlier had itExpand
Unique continuation and absence of positive eigenvalues for Schrodinger operators
On considere l'operateur de Laplace Δ sur R n et une fonction V(x) sur un sous-ensemble connexe, ouvert Ω de R n . On montre que si n≥3, une propriete de prolongement unique est vraie pour V∈L locExpand
On minimal support properties of solutions of Schr\"odinger equations
In this paper we obtain minimal support properties of solutions of Schr\"odinger equations. We improve previously known conditions on the potential for which the measure of the support of solutionsExpand
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