Related papers: Free Boundary Problems: The Forefront of Current a…
We study obstacle problems governed by two distinct types of diffusion operators involving interacting free boundaries. We obtain a somewhat surprising coupling property, leading to a comprehensive analysis of the free boundary. More…
In this paper, we use various ansatzes with undetermined functions and the technique of moving frame to find solutions with parameter functions modulo the Lie point symmetries for the classical non-steady boundary layer problems. These…
Background Independence is the modern form of the relational side of the Absolute versus Relational Debate. Difficulties with its implementation form the Problem of Time. Its 9 facets - Isham and Kucha\v{r}'s conceptual classification -…
The main result of this paper concerns the behavior of a free boundary arising from a minimization problem, close to the fixed boundary in two dimensions.
In 2007 an international conference engaged a reflection on the present conditions for sciences and scientific practice, to initiate a dialogue between science, philosophy, epistemology and sociology. Starting from many examples taken from…
The aim of this paper is first to give necessary and sufficient condition of existence (of free boundaries) for both Laplacian and bi-Laplacian operators in the case where the overdetermined condition is not constant. second, by using some…
In this paper we prove local interior and boundary Lipschitz continuity of solutions of a free boundary problem involving the $A$-Laplacian. We also show that the free boundary is represented locally by graphs of a family of lower…
I lay out the problem of time facets as arising piecemeal from a number of aspects of background independence. Almost all of these already have simpler classical counterparts. This approach can be viewed as a facet by facet completion of…
This essay examines the relationship between artificial intelligence and the historical evolution of modern Mathematics. Rather than viewing AI as an external rupture, we argue that its effectiveness reveals a structural tendency already…
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface…
We develop an existence and regularity theory for a class of degenerate one-phase free boundary problems. In this way we unify the basic theories in free boundary problems like the classical one-phase problem, the obstacle problem, or more…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
In this work we investigate the following isoperimetric problem: to find the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the area of the part of the boundary contained in…
The theory of boundary regularity for $p$-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality, $1<p<\infty$. The barrier classification of regular…
I report on the research activities performed under the (italian) MURST-PRIN project "Fisica Teorica del Nucleo e dei sistemi a pi\'u corpi" covering part of the topics on hadronic degrees of freedom. The most recent achievements in the…
In this note we present a survey concerning parabolic free boundary problems involving a discontinuous hysteresis operator. Such problems describe biological and chemical processes "with memory" in which various substances interact…
Arguably, the first bridge between vast, ancient, but disjoint domains of mathematical knowledge, - topology and number theory, - was built only during the last fifty years. This bridge is the theory of spectra in stable homotopy theory.…
These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free…
Robotics is called to be the next technological revolution and estimations indicate that it will trigger the fourth industrial revolution. This article presents a review of some of the most relevant milestones that occurred in robotics over…
The formulation of integrable models with open boundary conditions and the functional relations of fused transfer matrices are discussed. It is shown that finite-size corrections to the transfer matrices and unitarity relations of free…