# Matteo Dalla Riva PhD

Mathematics Keplinger Hall 3105 918-631-3675

matteo-dallariva@utulsa.edu

## Biography

Matteo Dalla Riva is an Assistant Professor of Mathematics in the College of Engineering and Natural Sciences at The University of Tulsa

Ph.D., University of Padova

- Partial Differential Equations

- Potential Theory

- Perturbation problems

- Non linear problems

- Differential Equations

- Functional Analysis

- Potential Theory

- Measure Theory

The following may be selected publications rather than a comprehensive list.

## Journal Articles

M. Dalla Riva, M. Lanza de Cristoforis, and P. Musolino: Analytic dependence of volume potentials corresponding to a parametric family of fundamental solutions, Integral Equations Operator Theory, 82 (2015), 371–393.

M. Dalla Riva and G. Mishuris: Existence results for a nonlinear transmission problem, J. Math. Anal. Appl. 430 (2015), 718–741.

M. Dalla Riva and P. Musolino: Real analytic families of harmonic functions in a planar domain with a small hole, J. Math. Anal. Appl., 422 (2015), 37–55.

M. Dalla Riva, P. Musolino, and S. Rogosin: Series expansions for the solution of the Dirichlet problem in a planar domain with a small hole, Asymptot. Anal., to appear.

M. Dalla Riva and P. Musolino: A singularly perturbed nonlinear traction problem in a periodically perforated domain. A functional analytic approach. Math. Methods Appl. Sci., 37 (2014), 106–122.

M. Dalla Riva and P. Musolino: Harmonic functions in a domain with a small hole. A functional analytic approach, Electron. J. Differential Equations, (2014), 1–14.

M. Dalla Riva: A family of fundamental solutions of elliptic partial differential operators with real constant coefficients. Integral Equations Operator Theory, 76 (2013), 1–23.

M. Dalla Riva, W. Mai, T. Qian, M. Yan, and S. Saitoh: A matrix inequality for the inversions of the restrictions of a positive definite Hermitian matrix. Advances in Linear Algebra & Matrix Theory (ALAMT), (2013), 55–58.

M. Dalla Riva, J. Morais, and P. Musolino: A family of fundamental solutions of elliptic partial differential operators with quaternion constant coefficients. Math. Methods Appl. Sci., 36 (2013), 1569–1582.

M. Dalla Riva and P. Musolino: A singularly perturbed non-ideal transmission problem and application to the effective conductivity of a periodic composite. SIAM J. Appl. Math., 73 (2013), 24–46.

M. Dalla Riva: Stokes flow in a singularly perturbed exterior domain. Complex Variables Elliptic Equations, 58 (2013), 231–257.

M. Dalla Riva and S. Yakubovich: On a Riemann–Liouville fractional analog of the Laplace operator with positive energy integral. Integral Transforms Special Functions, 23 (2012), 277–295.

M. Dalla Riva: Energy integral of the Stokes flow in a singularly perturbed exterior domain. Opuscula Math., 32 (2012), 647–659.

M. Dalla Riva and P. Musolino: Real analytic families of harmonic functions in a domain with a small hole. J. Differential Equations, 252 (2012), 6337–6355.

M. Dalla Riva and M. Lanza de Cristoforis: Weakly singular and microscopically hypersingular load perturbation for a nonlinear traction boundary value problem. A functional analytic approach. Complex Anal. Operator Theory, 5 (2011), 811–833.

M. Dalla Riva and M. Lanza de Cristoforis: A perturbation result for the layer potentials of general second-order elliptic operators with constant coefficients. J. Appl. Functional Anal., 5 (2010), 10–30.

M. Dalla Riva and M. Lanza de Cristoforis: A singularly perturbed nonlinear traction boundary value problem for linearized elastostatics. A functional analytic approach. Analysis (Munich), 30 (2010), 67–92.

M. Dalla Riva and M. Lanza de Cristoforis: Hypersingularly perturbed loads for a nonlinear traction boundary value problem. A functional analytic approach. Eurasian Math. J., 1 (2010), 31–58.

M. Dalla Riva and M. Lanza de Cristoforis: Microscopically weakly singularly perturbed loads for a nonlinear traction boundary value problem. A functional analytic approach. Complex Variables Elliptic Equations, 55 (2010), 771–794.

## Conference Proceedings

M. Dalla Riva and P. Musolino: Energy integral of a nonlinear traction problem in a singu- larly perturbed periodically perforated domain. In T.Aliyev, A.Golberg, and S.V.Rogosin, editors, Complex Analysis and Potential Theory with applications, Proceedings of the 9th ISAAC Congress, Krakow, Poland 5-9 August, 2013, pp. 41–52, Cambridge Scientific Publishers, Cottenham, UK, 2014.

M. Dalla Riva and P. Musolino: Energy integral of the solution of a non-ideal transmission problem in a singularly perturbed periodic domain. In T.Aliyev, A.Golberg, and S.V.Rogosin, editors, Complex Analysis and Potential Theory with applications, Proceedings of the 9th ISAAC Congress, Krakow, Poland 5-9 August, 2013, pp. 31–40, Cambridge Scientific Publishers, Cottenham, UK, 2014.

M. Dalla Riva and P. Musolino: Harmonic functions in a domain with a small hole. A functional analytic approach. In Integral Methods in Science and Engineering: Theoretical and Computational Advances, Proceedings of the 13th International Conference on Integral Methods in Science and Engineering, IMSE 2014, Karlsruhe, Germany 21-25 July 2014, Springer, Basel, to appear.

M. Dalla Riva, M. Lanza de Cristoforis, and P. Musolino: On a singularly perturbed periodic nonlinear Robin problem. Analytical Methods of Analysis and Differential Equations: AMADE-2012, Cambridge Scientific Publishers, Cottenham, UK, 2014, pp. 73–92.

M. Dalla Riva and P. Musolino: Effective conductivity of a singularly perturbed periodic two- phase composite with imperfect thermal contact at the two-phase interface. Ninth International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2012, Vienna, Austria, July 10–14, 2012, AIP Conference Proceedings vol. 1493, S. Sivasundaram (Ed.), American Institute of Physics, Melville, NY, 2012, pp. 264–268.

M. Dalla Riva, J. Morais, and P. Musolino: A family of fundamental solutions for elliptic quaternion coefficient differential operators and application to perturbation results for single layer potentials. Proceedings of the Ninth International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2012, Vienna, Austria, July 10–14, 2012, AIP Conference Proceedings vol. 1493, S. Sivasundaram (Ed.), American Institute of Physics, Melville, NY, 2012, pp. 269–273.

M. Dalla Riva and M. Lanza de Cristoforis: Singularly perturbed loads for a nonlinear traction boundary value problem on a singularly perturbed domain. Progress in Analysis and Its Applications, Proceedings of the 7th International ISAAC Congress, Imperial College London, July 13–18, 2009, M. Ruzhansky and J. Wirth (Eds.), World Scientific Publishers, Hackensack, NJ, 2010, pp. 31–38.

M. Dalla Riva: Microscopic behavior of the Stokes flow in a singularly perturbed exterior domain. Progress in Analysis and Its Applications, Proceedings of the 7th International ISAAC Congress, Imperial College London, July 13–18, 2009, M. Ruzhansky and J. Wirth (Eds.), World Scientific Publishers, Hackensack, NJ, 2010, pp. 23–30.

M. Dalla Riva: The layer potential of some partial differential operators: real analytic dependence upon perturbations. Further Progress in Analysis, Proceedings of the 6th International ISAAC Congress, Ankara, Turkey, August 13–18, 2007, World Scientific, Singapore, 2009, pp. 208–217.

## Other

M. Dalla Riva: Potential theoretic methods for the analysis of singularly perturbed problems in linearized elasticity, University of Padova. Supervisor: M. Lanza de Cristoforis (128 pp.), 2008.

MATH 3073 Differential Equations