Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems

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Standard

Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems. / Abels, Helmut; Grubb, Gerd; Wood, Ian Geoffrey.

I: Journal of Functional Analysis, Bind 266, Nr. 7, 2014, s. 4037-4100.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Abels, H, Grubb, G & Wood, IG 2014, 'Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems', Journal of Functional Analysis, bind 266, nr. 7, s. 4037-4100. https://doi.org/10.1016/j.jfa.2014.01.016

APA

Abels, H., Grubb, G., & Wood, I. G. (2014). Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems. Journal of Functional Analysis, 266(7), 4037-4100. https://doi.org/10.1016/j.jfa.2014.01.016

Vancouver

Abels H, Grubb G, Wood IG. Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems. Journal of Functional Analysis. 2014;266(7):4037-4100. https://doi.org/10.1016/j.jfa.2014.01.016

Author

Abels, Helmut ; Grubb, Gerd ; Wood, Ian Geoffrey. / Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems. I: Journal of Functional Analysis. 2014 ; Bind 266, Nr. 7. s. 4037-4100.

Bibtex

@article{bd36bd6c68dd410aa5298b961f20d44c,
title = "Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems",
abstract = "The theory of selfadjoint extensions of symmetric operators, and more generally the theory of extensions of dual pairs, was implemented some years ago for boundary value problems for elliptic operators on smooth bounded domains. Recently, the questions have been taken up again for nonsmooth domains. In the present work we show that pseudodifferential methods can be used to obtain a full characterization, including Kreĭn resolvent formulas, of the realizations of nonselfadjoint second-order operators on <img height={"}16{"} border={"}0{"} style={"}vertical-align:bottom{"} width={"}40{"} alt={"}View the MathML source{"} title={"}View the MathML source{"} src={"}http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022123614000342-si1.gif{"}>C32+ε domains; more precisely, we treat domains with <img height={"}26{"} border={"}0{"} style={"}vertical-align:bottom{"} width={"}31{"} alt={"}View the MathML source{"} title={"}View the MathML source{"} src={"}http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022123614000342-si2.gif{"}>Bp,232-smoothness and operators with <img height={"}20{"} border={"}0{"} style={"}vertical-align:bottom{"} width={"}23{"} alt={"}View the MathML source{"} title={"}View the MathML source{"} src={"}http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022123614000342-si3.gif{"}>Hq1-coefficients, for suitable p>2(n−1)p>2(n−1) and q>nq>n. The advantage of the pseudodifferential boundary operator calculus is that the operators are represented by a principal part and a lower-order remainder, leading to regularity results; in particular we analyze resolvents, Poisson solution operators and Dirichlet-to-Neumann operators in this way, also in Sobolev spaces of negative order.",
author = "Helmut Abels and Gerd Grubb and Wood, {Ian Geoffrey}",
year = "2014",
doi = "10.1016/j.jfa.2014.01.016",
language = "English",
volume = "266",
pages = "4037--4100",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press",
number = "7",

}

RIS

TY - JOUR

T1 - Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems

AU - Abels, Helmut

AU - Grubb, Gerd

AU - Wood, Ian Geoffrey

PY - 2014

Y1 - 2014

N2 - The theory of selfadjoint extensions of symmetric operators, and more generally the theory of extensions of dual pairs, was implemented some years ago for boundary value problems for elliptic operators on smooth bounded domains. Recently, the questions have been taken up again for nonsmooth domains. In the present work we show that pseudodifferential methods can be used to obtain a full characterization, including Kreĭn resolvent formulas, of the realizations of nonselfadjoint second-order operators on <img height="16" border="0" style="vertical-align:bottom" width="40" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022123614000342-si1.gif">C32+ε domains; more precisely, we treat domains with <img height="26" border="0" style="vertical-align:bottom" width="31" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022123614000342-si2.gif">Bp,232-smoothness and operators with <img height="20" border="0" style="vertical-align:bottom" width="23" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022123614000342-si3.gif">Hq1-coefficients, for suitable p>2(n−1)p>2(n−1) and q>nq>n. The advantage of the pseudodifferential boundary operator calculus is that the operators are represented by a principal part and a lower-order remainder, leading to regularity results; in particular we analyze resolvents, Poisson solution operators and Dirichlet-to-Neumann operators in this way, also in Sobolev spaces of negative order.

AB - The theory of selfadjoint extensions of symmetric operators, and more generally the theory of extensions of dual pairs, was implemented some years ago for boundary value problems for elliptic operators on smooth bounded domains. Recently, the questions have been taken up again for nonsmooth domains. In the present work we show that pseudodifferential methods can be used to obtain a full characterization, including Kreĭn resolvent formulas, of the realizations of nonselfadjoint second-order operators on <img height="16" border="0" style="vertical-align:bottom" width="40" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022123614000342-si1.gif">C32+ε domains; more precisely, we treat domains with <img height="26" border="0" style="vertical-align:bottom" width="31" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022123614000342-si2.gif">Bp,232-smoothness and operators with <img height="20" border="0" style="vertical-align:bottom" width="23" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022123614000342-si3.gif">Hq1-coefficients, for suitable p>2(n−1)p>2(n−1) and q>nq>n. The advantage of the pseudodifferential boundary operator calculus is that the operators are represented by a principal part and a lower-order remainder, leading to regularity results; in particular we analyze resolvents, Poisson solution operators and Dirichlet-to-Neumann operators in this way, also in Sobolev spaces of negative order.

U2 - 10.1016/j.jfa.2014.01.016

DO - 10.1016/j.jfa.2014.01.016

M3 - Journal article

VL - 266

SP - 4037

EP - 4100

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 7

ER -

ID: 102114363