Search results for "Mathematica"
showing 10 items of 7971 documents
Maximal regularity via reverse Hölder inequalities for elliptic systems of n-Laplace type involving measures
2008
In this note, we consider the regularity of solutions of the nonlinear elliptic systems of n-Laplacian type involving measures, and prove that the gradients of the solutions are in the weak Lebesgue space Ln,∞. We also obtain the a priori global and local estimates for the Ln,∞-norm of the gradients of the solutions without using BMO-estimates. The proofs are based on a new lemma on the higher integrability of functions.
Regular solutions of transmission and interaction problems for wave equations
1989
Consider n bounded domains Ω ⊆ ℝ and elliptic formally symmetric differential operators A1 of second order on Ωi Choose any closed subspace V in , and extend (Ai)i=1,…,n by Friedrich's theorem to a self-adjoint operator A with D(A1/2) = V (interaction operator). We give asymptotic estimates for the eigenvalues of A and consider wave equations with interaction. With this concept, we solve a large class of problems including interface problems and transmission problems on ramified spaces.25,32 We also treat non-linear interaction, using a theorem of Minty29.
A group analysis via weak equivalence transformations for a model of tumor encapsulation
2004
A symmetry reduction of a PDEs system, describing the expansive growth of a benign tumour, is obtained via a group analysis approach. The presence in the model of three arbitrary functions suggests the use of Lie symmetries by using the weak equivalence transformations. An invariant classification is given which allows us to reduce the initial PDEs system to an ODEs system. Numerical simulations show a realistic enough description of the physical process.
Unifying vectors and matrices of different dimensions through nonlinear embeddings
2020
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous parameter $\kappa \in \mathbb{R}$ is being varied, thus allowing the unification of vectors, matrices and tensors in single mathematical structures. This technique is applied to construct warped models in the passage from supergravity in 10 or 11-dimensional spacetimes to 4-dimensional ones. We also show how nonlinear embeddings can be used to connect cellular automata (CAs) to coupled map lattices (CMLs) and to nonlinear partial differential equations, derivi…
Gibbs states, algebraic dynamics and generalized Riesz systems
2020
In PT-quantum mechanics the generator of the dynamics of a physical system is not necessarily a self-adjoint Hamiltonian. It is now clear that this choice does not prevent to get a unitary time evolution and a real spectrum of the Hamiltonian, even if, most of the times, one is forced to deal with biorthogonal sets rather than with on orthonormal basis of eigenvectors. In this paper we consider some extended versions of the Heisenberg algebraic dynamics and we relate this analysis to some generalized version of Gibbs states and to their related KMS-like conditions. We also discuss some preliminary aspects of the Tomita-Takesaki theory in our context.
Nonexistence of global weak solutions for a nonlinear Schrodinger equation in an exterior domain
2020
We study the large-time behavior of solutions to the nonlinear exterior problem L u ( t , x ) = &kappa
A C0-Semigroup of Ulam Unstable Operators
2020
The Ulam stability of the composition of two Ulam stable operators has been investigated by several authors. Composition of operators is a key concept when speaking about C0-semigroups. Examples of C0-semigroups formed with Ulam stable operators are known. In this paper, we construct a C0-semigroup (Rt)t&ge
Ulam Stability for the Composition of Operators
2020
Working in the setting of Banach spaces, we give a simpler proof of a result concerning the Ulam stability of the composition of operators. Several applications are provided. Then, we give an example of a discrete semigroup with Ulam unstable members and an example of Ulam stable operators on a Banach space, such that their sum is not Ulam stable. Another example is concerned with a C 0 -semigroup ( T t ) t &ge
The General Stokes’s Theorem
2012
Let ω be a differential form of degree k - 1 and class C 1 in a neighborhood of a compact regular k-surface with boundary M of class C 2. The general Stokes’s theorem gives a relationship between the integral of ω over the boundary of M and the integral of the exterior differential dω over M. It can be viewed as a generalization of Green’s theorem to higher dimensions, and it plays a role not unlike that of the fundamental theorem of calculus in an elementary course of analysis. Particular cases of the general Stokes’s theorem that are of great importance are the divergence theorem, which relates a triple integral with a surface integral and what we know as the classical Stokes’s theorem, w…
Lipschitz classes and the Hardy-Littlewood property
1993
We study the geometry of plane domains and the uniform Holder continuity properties of analytic functions.