Singularly perturbed boundary value problems
M Dalla Riva, M Lanza de Cristoforis… - A Functional Analytic …, 2021 - Springer
This book is the first introductory and self-contained presentation of a method for the
analysis of singularly perturbed boundary value problems that we have called the Functional …
analysis of singularly perturbed boundary value problems that we have called the Functional …
Classes of kernels and continuity properties of the double layer potential in Hölder spaces
M Lanza de Cristoforis - Integral Equations and Operator Theory, 2023 - Springer
We prove the validity of regularizing properties of the boundary integral operator
corresponding to the double layer potential associated to the fundamental solution of a …
corresponding to the double layer potential associated to the fundamental solution of a …
Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients
A Barton - manuscripta mathematica, 2016 - Springer
This paper considers the theory of higher-order divergence-form elliptic differential
equations. In particular, we provide new generalizations of several well-known tools from the …
equations. In particular, we provide new generalizations of several well-known tools from the …
Regularizing properties of the double layer potential of second order elliptic differential operators
F Dondi, ML de Cristoforis - arXiv preprint arXiv:2103.06971, 2021 - arxiv.org
We prove the validity of regularizing properties of a double layer potential associated to the
fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator …
fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator …
On the tangential gradient of the kernel of the double layer potential
ML de Cristoforis - Complex Variables and Elliptic Equations, 2024 - Taylor & Francis
In this paper, we consider an elliptic operator with constant coefficients and we estimate the
maximal function of the tangential gradient of the kernel of the double layer potential with …
maximal function of the tangential gradient of the kernel of the double layer potential with …
A nonvariational form of the Neumann problem for H\"{o} lder continuous harmonic functions
ML de Cristoforis - arXiv preprint arXiv:2403.15057, 2024 - arxiv.org
We present a nonvariational setting for the Neumann problem for harmonic functions that
are H\"{o} lder continuous and that may have infinite Dirichlet integral. Then we introduce a …
are H\"{o} lder continuous and that may have infinite Dirichlet integral. Then we introduce a …
Higher-order elliptic equations in non-smooth domains: a partial survey
A Barton, S Mayboroda - … Complex Analysis, Banach Spaces, and Operator …, 2016 - Springer
Recent years have brought significant advances in the theory of higher-order elliptic
equations in non-smooth domains. Sharp pointwise estimates on derivatives of …
equations in non-smooth domains. Sharp pointwise estimates on derivatives of …
A family of fundamental solutions of elliptic partial differential operators with quaternion constant coefficients
M Dalla Riva, J Morais… - Mathematical Methods in …, 2013 - Wiley Online Library
The purpose of this paper is to construct a family of fundamental solutions for elliptic partial
differential operators with quaternion constant coefficients. The elements of such family are …
differential operators with quaternion constant coefficients. The elements of such family are …
A survey on the boundary behavior of the double layer potential in Schauder spaces in the frame of an abstract approach
M Lanza de Cristoforis - … Solutions for Mathematical Models in Science …, 2024 - Springer
We provide a summary of the continuity properties of the boundary integral operator
corresponding to the double layer potential that is associated to the fundamental solution of …
corresponding to the double layer potential that is associated to the fundamental solution of …
Continuity of the double layer potential of a second order elliptic differential operator in Schauder spaces on the boundary
ML de Cristoforis - arXiv preprint arXiv:2305.19672, 2023 - arxiv.org
We prove the validity of a regularizing property on the boundary of the double layer potential
associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic …
associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic …