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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.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Boundary Value Problems for Second-Order Elliptic Equations and Related Topics =/
其他題名:	Problemas de valores en la frontera para operadores elipticos de segundo orden y topicos relacionados.
其他題名:	Problemas de valores en la frontera para operadores elipticos de segundo orden y topicos relacionados.
作者:	Poggi Cevallos, Bruno Giuseppe.
面頁冊數:	1 online resource (474 pages)
附註:	Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
Contained By:	Dissertations Abstracts International83-02B.
標題:	Mathematics. -
電子資源:	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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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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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
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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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