Andrew Morris

Accepting PhD Students

PhD projects

Andrew Morris' research concerns the development of modern techniques in harmonic analysis, functional calculus and geometric measure theory for application to partial differential equations on Riemannian manifolds and rough domains. This includes elliptic systems with rough coefficients, local T(b) techniques, first-order methods, quadratic estimates, holomorphic functional calculus, singular integral theory, layer potentials, Hardy spaces, boundary value problems and uniform rectifiability.

Dr Morris is interested in supervising postgraduate research students in harmonic analysis, operator theory and partial differential equations.

Research activity per year

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7 Article

Solvability for non-smooth Schrödinger equations with singular potentials and square integrable data
Morris, A. & Turner, A., 1 Jan 2025, In: Journal of Functional Analysis. 288, 1, 95 p., 110680.
Research output: Contribution to journal › Article › peer-review

Open Access
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21 Downloads (Pure)
Quadratic estimates for degenerate elliptic systems on manifolds with lower Ricci curvature bounds and boundary value problems
Auscher, P., Morris, A. & Rosén, A., 20 May 2022, (Accepted/In press) In: Communications in Analysis and Geometry.
Research output: Contribution to journal › Article › peer-review

Open Access
10 Downloads (Pure)
Unboundedness of potential dependent Riesz transforms for totally irregular measures
Bailey, J., Morris, A. & Reguera, M. C., 1 Feb 2021, In: Journal of Mathematical Analysis and Applications. 494, 1, 32 p., 124570.
Research output: Contribution to journal › Article › peer-review

Open Access
File

1 Citation (Scopus)

156 Downloads (Pure)
Carleson measure estimates and the Dirichlet problem for degenerate elliptic equations
Hofmann, S., Le, P. & Morris, A., 28 Oct 2019, In: Analysis and PDE. 12, 8, p. 2095-2146 52 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
1 Citation (Scopus)

287 Downloads (Pure)
L^p-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets
Hofmann, S., Mitrea, D., Mitrea, M. & Morris, A., Jan 2017, In: Memoirs of the American Mathematical Society. 245, 1159, p. 1-108 108 p.
Research output: Contribution to journal › Article › peer-review

Open Access
File
15 Citations (Scopus)

273 Downloads (Pure)

1 Finished

Eliminating symmetry and permitting singularity in periodic homogenization
Morris, A. (Principal Investigator)
The Royal Society
18/03/20 → 17/03/24
Project: Research Councils

Andrew Morris

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Collaborations and top research areas from the last five years

Dive into details

Solvability for non-smooth Schrödinger equations with singular potentials and square integrable data

Quadratic estimates for degenerate elliptic systems on manifolds with lower Ricci curvature bounds and boundary value problems

Unboundedness of potential dependent Riesz transforms for totally irregular measures

Carleson measure estimates and the Dirichlet problem for degenerate elliptic equations

L^p-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets

Eliminating symmetry and permitting singularity in periodic homogenization

Andrew Morris

Fingerprint

Collaborations and top research areas from the last five years

Research output

Solvability for non-smooth Schrödinger equations with singular potentials and square integrable data

Quadratic estimates for degenerate elliptic systems on manifolds with lower Ricci curvature bounds and boundary value problems

Unboundedness of potential dependent Riesz transforms for totally irregular measures

Carleson measure estimates and the Dirichlet problem for degenerate elliptic equations

Lp-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets

Projects

Eliminating symmetry and permitting singularity in periodic homogenization

L^p-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets