Hölder Regularity for Solutions of Ultraparabolic Equations in Divergence Form

By Sergio Polidoro, M. Alessandra Ragusa. 2001

60 citations recorded by the source corpus.

AbstractWe consider the second order differential equation $$\sum\limits_{i,j = 1}^{m_0 } {\partial _{x_i } (a_{i,j} (x,t)\partial _{x_j } u) + \sum\limits_{i,j = 1}^N {b_{i,j} x_i \partial _{x_j } u - \partial _t u = \sum\limits_{j = 1}^{m_0 } {\partial _{x_j } F_j (x,t)} } } $$ , where (x,t)∈ℝN+1, 0<m0⩽N, the coefficients ai,j belong to a suitable space of vanishing mean oscillation functions VMOL and B=(bi,j) is a constant real matrix. The aim of this paper is to study interior regularity for weak solutions to the above equation assuming that Fj belong to a function space of Morrey type.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/03216d215edcae69a4297745a952375b7e775d08

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In Applied Mathematics

1. Francesca Anceschi
2. Sergio Polidoro
3. C. Imbert
4. Luis Silvestre

In Mathematical Physics

1. Francesca Anceschi
2. Sergio Polidoro

Citations in the corpus

• A survey on the classical theory for Kolmogorov equation (2019, methodology): “Operators with VMO coefficients ai j have been studied in [16] by Bramanti, Cerutti and Manfredini, [57] by Manfredini and Polidoro, and in [65], [66] by Polidoro and Ragusa.”