Former Research Group
Rigidity and Flexibility in PDEs
The main focus of the research group was on different types of rigidity properties in PDEs including:
- nonlocal PDEs with an emphasis on unique continuation problems, regularity theory and applications to inverse and control problems,
- elliptic and parabolic free boundary problems of obstacle type,
- non-convex problems in the calculus of variations and in elasticity, in particular motivated by problems arising in the modelling of shape-memory alloys.
Research Group Leader
01.10.17
31.03.20
Angkana Rüland
Universität Heidelberg
Publications
inJournal
2022Bounds on the first Betti number : an approach via Schatten norm estimates on semigroup differences
In: The journal of geometric analysisinJournal
2022On Runge approximation and Lipschitz stability for a finite-dimensional Schrödinger inverse problem
In: Applicable analysis : an international journalinJournal
2021On a probabilistic model for martensitic avalanches incorporating mechanical compatibility
In: NonlinearityinJournal
2021Discrete Carleman estimates and three balls inequalities
In: Calculus of variations and partial differential equationsinJournal
2021Exceptional Legendre polynomials and confluent Darboux transformations
In: Symmetry, integrability and geometry : methods and applications (SIGMA)inJournal
2020The Calderón problem for the fractional Schrödinger equation with drift
In: Calculus of variations and partial differential equationsinJournal
2020Exact constructions in the (non-linear) planar theory of elasticity : from elastic crystals to nematic elastomers
In: Archive for rational mechanics and analysisinJournal
2020Convex integration solutions for the geometrically non-linear two-well problem with higher Sobolev regularity
In: Mathematical models and methods in applied sciencesinJournal
2020On non stress-free junctions between martensitic plates
In: Interfaces and free boundariesinJournal
2020On two methods for quantitative unique continuation results for some nonlocal operators
In: Communications in partial differential equationsinJournal
2020Uniqueness and reconstruction for the fractional Calderón problem with a single measurement
In: Journal of functional analysisinJournal
2020The Calderón problem for a space-time fractional parabolic equation
In: SIAM journal on mathematical analysisinBook
2020Manifolds with Ricci curvature in the Kato class : heat kernel bounds and applications
In: Analysis and geometry on graphs and manifoldsinJournal
2020Higher Sobolev regularity of convex integration solutions in elasticity : the planar geometrically linearized hexagonal-to-rhombic phase transformation
In: Journal of elasticityinJournal
2020Quantitative approximation properties for the fractional heat equation
In: Mathematical control and related fieldsinJournal
2020The fractional Calderón problem : low regularity and stability
In: Nonlinear analysis / AinJournal
2019A model for the evolution of highly reversible martensitic transformations
In: Mathematical models and methods in applied sciencesinJournal
2019Analysis of a moving mask hypothesis for martensitic transformations
In: Journal of nonlinear scienceinJournal
2019Approximation theorems for parabolic equations and movement of local hot spots
In: Duke mathematical journalinJournal
2019