Second order elliptic equations with mixed boundary conditions

Pryde, A. J.

doi:10.1016/0022-247x(81)90102-5

Cited by 33 publications

(16 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proof of our main result is presented later on in Section 8. Our proof bases on an interpolation argument going back to Pryde [36]. The same idea has been utilized in [6].…”

Section: Introductionmentioning

confidence: 99%

The Kato Square Root Problem for mixed boundary conditions

Egert

Haller-Dintelmann

Tolksdorf

2014

Journal of Functional Analysis

View full text Add to dashboard Cite

Abstract. We consider the negative Laplacian subject to mixed boundary conditions on a bounded domain. We prove under very general geometric assumptions that slightly above the critical exponent 1 2 its fractional power domains still coincide with suitable Sobolev spaces of optimal regularity. In combination with a reduction theorem recently obtained by the authors, this solves the Kato Square Root Problem for elliptic second order operators and systems in divergence form under the same geometric assumptions. Thereby we answer a question posed by J. L. Lions in 1962 [29].

show abstract

“…The proof of our main result is presented later on in Section 8. Our proof bases on an interpolation argument going back to Pryde [36]. The same idea has been utilized in [6].…”

Section: Introductionmentioning

confidence: 99%

The Kato Square Root Problem for mixed boundary conditions

Egert

Haller-Dintelmann

Tolksdorf

2014

Journal of Functional Analysis

View full text Add to dashboard Cite

show abstract

“…It has been investigated extensively from the functional analytic point of view [20,25,26,29]. However, there are only some preliminary results [2,3,6] available concerning the heat trace asymptotics.…”

Section: Introductionmentioning

confidence: 99%

On Properties of the Asymptotic Expansion of the Heat Trace for the N/D Problem

2001

View full text Add to dashboard Cite

show abstract

“…By a standard stopping time argument as used in [3,Section 5], in order to prove (17) it suffices to prove the following claim.…”

Section: 4mentioning

confidence: 99%

“…Suppose that J A satisfies the following coercivity condition: there exists κ > 0 such that and [17] for specific material on forms such as J A and further references to mixed boundary value problems. The Kato square root problem is to determine whether the domain D √ L A = V. The Kato square root problem for second order elliptic operators on Ω = R n was solved in [3] by P. Auscher, S. Hofmann, M. Lacey, A. M c Intosh and Ph.…”

Section: Introductionmentioning

confidence: 99%