Maximal parabolic regularity for divergence operators including mixed boundary conditions

By Robert Haller-Dintelmann, Joachim Rehberg. 2008

108 citations recorded by the source corpus.

We show that elliptic second order operators $A$ of divergence type fulfill maximal parabolic regularity on distribution spaces, even if the underlying domain is highly non-smooth, the coefficients of $A$ are discontinuous and $A$ is complemented with mixed boundary conditions. Applications to quasilinear parabolic equations with non-smooth data are presented.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6471c9efef2035c423b822a09d599698999dc10f

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In Applied Mathematics

1. Robert Haller-Dintelmann
2. Joachim Rehberg
3. Alf Jonsson
4. Dorothee Knees
5. P. Auscher
6. N. Badr
7. Mark Veraar
8. C. Gallarati

In Computational Theory and Mathematics

1. Robert Haller-Dintelmann
2. Alf Jonsson
3. Dorothee Knees
4. Joachim Rehberg
5. P. Auscher
6. Mark Veraar
7. C. Gallarati

In Mathematical Physics

1. Alf Jonsson
2. Dorothee Knees
3. Robert Haller-Dintelmann
4. Joachim Rehberg
5. P. Auscher
6. N. Badr
7. Mark Veraar
8. C. Gallarati

Citations in the corpus

• The square root problem for second-order, divergence form operators with mixed boundary conditions on Lp (2012, background): “Consequences In this section we come back to the original motivation of our work, namely to carry over results which are known for divergence operators, when acting on L spaces, to the spaces from the scale W D , q ∈ [2,∞[, compare also [9], [25, Section 5], [35], [37].”
• Maximal Regularity for Non-autonomous Equations with Measurable Dependence on Time (2014, background): “ mapping principle [4, 6, 14, 16, 67, 81]. This has found numerous applications in problems from mathematical physics (e.g. fluid dynamics, reaction-diffusion equations, material science, etc. see e.g. [1, 14, 21, 35, 44, 63, 71, 70, 79, 81, 84, 85, 95]). For maximal Ho¨lder-regularity we refer the re”
• Elliptic and parabolic regularity for second‐ order divergence operators with mixed boundary conditions (2013, methodology): “ operators, well-known from smooth constellations, were re-established. This concerns elliptic regularity (in particular Holder continuity) [26], [22], [25], [28], maximal parabolic regularity [23], [29], [31] and interpolation [24]. In this paper, we impose more general conditions on the domain and”