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Boundary Value Problems for Second-Order Elliptic Equations and Related Topics = = Problemas de valores en la frontera para operadores elipticos de segundo orden y topicos relacionados.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Boundary Value Problems for Second-Order Elliptic Equations and Related Topics =/
Reminder of title:	Problemas de valores en la frontera para operadores elipticos de segundo orden y topicos relacionados.
remainder title:	Problemas de valores en la frontera para operadores elipticos de segundo orden y topicos relacionados.
Author:	Poggi Cevallos, Bruno Giuseppe.
Description:	1 online resource (474 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
Contained By:	Dissertations Abstracts International83-02B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28496050click for full text (PQDT)
ISBN:	9798534688207

Boundary Value Problems for Second-Order Elliptic Equations and Related Topics = = Problemas de valores en la frontera para operadores elipticos de segundo orden y topicos relacionados.
Poggi Cevallos, Bruno Giuseppe.

Boundary Value Problems for Second-Order Elliptic Equations and Related Topics =Problemas de valores en la frontera para operadores elipticos de segundo orden y topicos relacionados.Problemas de valores en la frontera para operadores elipticos de segundo orden y topicos relacionados. - 1 online resource (474 pages)

Source: Dissertations Abstracts International, Volume: 83-02, Section: B.

Thesis (Ph.D.)--University of Minnesota, 2021.

Includes bibliographical references

We study perturbation results for boundary value problems for second-order elliptic partial differential equations, and the exponential decay of solutions to generalized Schrödinger operators. First, through the use of sawtooth domains and the extrapolation technique of Carleson measures, we show the stability of the solvability of the Dirichlet problem for (additive) Carleson perturbations of certain degenerate elliptic operators −divA∇ on domains with low dimensional boundaries (joint work with S. Mayboroda). Then, with a different method of proof, we expand these perturbation results to more abstract domains (including some domains with mixed-dimensional boundaries) and a broader type of Carleson perturbation, yielding some new applications (including to free boundary problems) (joint work with J. Feneuil). Next, together with S. Bortz, S. Hofmann, J.L. Luna García, and S. Mayboroda, we consider the uniformly elliptic operators L=−div(A∇+B1) +B2∇+V on the upper half space Rn+1+=Rn×{t >0},n≥3, with t-independent coefficients, and we prove the L² solvability of the Dirichlet, Neumann and Regularity problems under the condition that |B1|,|B2|,|V|² have small Ln(Rn) norm. Finally, we show that for generalized magnetic Schrödinger operators −(∇−ia)TA(∇−ia) +V, with certain conditions providing an uncertainty principle, resolvents and Lax-Milgram solutions exhibit exponential decay (in an L²-sense), and we improve these estimates to upper pointwise exponential decay for the magnetic Schrödinger operator -(∇−ia)², and to sharp (that is, upper and lower) pointwise exponential decay for the Schrödinger operator on a non-homogeneous medium −divA∇+V (joint work with S. Mayboroda).

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798534688207Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Boundary value problemsIndex Terms--Genre/Form:

542853
Electronic books.

Boundary Value Problems for Second-Order Elliptic Equations and Related Topics = = Problemas de valores en la frontera para operadores elipticos de segundo orden y topicos relacionados.
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502 $a Thesis (Ph.D.)--University of Minnesota, 2021.
504 $a Includes bibliographical references
520 $a We study perturbation results for boundary value problems for second-order elliptic partial differential equations, and the exponential decay of solutions to generalized Schrödinger operators. First, through the use of sawtooth domains and the extrapolation technique of Carleson measures, we show the stability of the solvability of the Dirichlet problem for (additive) Carleson perturbations of certain degenerate elliptic operators −divA∇ on domains with low dimensional boundaries (joint work with S. Mayboroda). Then, with a different method of proof, we expand these perturbation results to more abstract domains (including some domains with mixed-dimensional boundaries) and a broader type of Carleson perturbation, yielding some new applications (including to free boundary problems) (joint work with J. Feneuil). Next, together with S. Bortz, S. Hofmann, J.L. Luna García, and S. Mayboroda, we consider the uniformly elliptic operators L=−div(A∇+B1) +B2∇+V on the upper half space Rn+1+=Rn×{t >0},n≥3, with t-independent coefficients, and we prove the L² solvability of the Dirichlet, Neumann and Regularity problems under the condition that |B1|,|B2|,|V|² have small Ln(Rn) norm. Finally, we show that for generalized magnetic Schrödinger operators −(∇−ia)TA(∇−ia) +V, with certain conditions providing an uncertainty principle, resolvents and Lax-Milgram solutions exhibit exponential decay (in an L²-sense), and we improve these estimates to upper pointwise exponential decay for the magnetic Schrödinger operator -(∇−ia)², and to sharp (that is, upper and lower) pointwise exponential decay for the Schrödinger operator on a non-homogeneous medium −divA∇+V (joint work with S. Mayboroda).
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538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
650 4 $a Partial differential equations. $3 2180177
650 4 $a Conventions. $3 3562375
650 4 $a Boundary conditions. $3 3560411
650 4 $a Boundary value problems. $3 527599
650 4 $a Geometry. $3 517251
650 4 $a Manuscripts. $3 3566242
653 $a Boundary value problems
653 $a Dirichlet problem
653 $a Harmonic measure
653 $a Layer potentials
653 $a Partial differential equations
653 $a Schrodinger operators
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