What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Quantum mechanics
- Partial differential equation
His main research concerns Mathematical analysis, Nonlinear system, Heat equation, Porous medium and Uniqueness.
He combines subjects such as Inverse and Diffusion equation with his study of Mathematical analysis.
His research in Nonlinear system intersects with topics in Semigroup, Elliptic curve, Algebra, Thermal diffusivity and Space.
His studies in Heat equation integrate themes in fields like Initial value problem, Simultaneous equations, Sign, Statistical physics and Independent equation.
His Uniqueness research is multidisciplinary, incorporating elements of Mathematical proof, Combinatorics, Type, Symmetry in biology and Weak solution.
His Bounded function research is multidisciplinary, incorporating perspectives in Nonlinear heat equation, Function space, Pure mathematics and Domain.
His most cited work include:
- A Strong Maximum Principle for some quasilinear elliptic equations (927 citations)
- An $L^1$ -theory of existence and uniqueness of solutions of nonlinear elliptic equations (737 citations)
- The Porous Medium Equation: Mathematical Theory (612 citations)
What are the main themes of his work throughout his whole career to date?
The scientist’s investigation covers issues in Mathematical analysis, Bounded function, Nonlinear system, Porous medium and Heat equation.
His Diffusion equation research extends to Mathematical analysis, which is thematically connected.
His study in Bounded function is interdisciplinary in nature, drawing from both Pure mathematics, Mathematical physics, Dirichlet problem, Boundary value problem and Domain.
Juan Luis Vázquez has included themes like p-Laplacian and Laplace operator in his Pure mathematics study.
The Domain study combines topics in areas such as Zero and Dirichlet boundary condition.
His study on Nonlinear system also encompasses disciplines like
- Type that intertwine with fields like Limit,
- Degenerate energy levels which is related to area like Parabolic partial differential equation.
He most often published in these fields:
- Mathematical analysis (70.75%)
- Bounded function (25.00%)
- Nonlinear system (22.25%)
What were the highlights of his more recent work (between 2016-2021)?
- Mathematical analysis (70.75%)
- Bounded function (25.00%)
- Pure mathematics (14.00%)
In recent papers he was focusing on the following fields of study:
Mathematical analysis, Bounded function, Pure mathematics, Nonlinear system and Space are his primary areas of study.
In his works, Juan Luis Vázquez performs multidisciplinary study on Mathematical analysis and Porous medium.
His work carried out in the field of Bounded function brings together such families of science as Boundary value problem, Dirichlet conditions, Uniqueness, Domain and Laplace operator.
His Pure mathematics study combines topics in areas such as p-Laplacian and Scalar curvature.
His studies deal with areas such as Order, Logarithm, Statistical physics, Exponential function and Degenerate energy levels as well as Nonlinear system.
His Space study also includes
- Constant and related Function space, Sobolev space and Combinatorics,
- Nabla symbol that intertwine with fields like Compact space, Inverse, Balanced flow, Vortex and Viscosity solution.
Between 2016 and 2021, his most popular works were:
- Optimal existence and uniqueness theory for the fractional heat equation (54 citations)
- The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (50 citations)
- Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations (39 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Quantum mechanics
- Geometry
Juan Luis Vázquez mainly investigates Bounded function, Mathematical analysis, Pure mathematics, Domain and Nonlinear system.
The concepts of his Bounded function study are interwoven with issues in Omega, Measure, Dirichlet conditions, Uniqueness and Degenerate energy levels.
Juan Luis Vázquez merges Mathematical analysis with Porous medium in his study.
His work deals with themes such as Smoothness and Laplace operator, which intersect with Pure mathematics.
His Domain research is multidisciplinary, incorporating perspectives in Zero and Fractional Laplacian.
He has researched Nonlinear system in several fields, including Dimension, Mathematical physics, Logarithmic scale, Fractional diffusion and Sigma.
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