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laplacian
100%
solutions
99%
space
69%
lie groups
67%
equations
62%
heat
59%
geometry
38%
norm
37%
differential equations
37%
euclidean space
33%
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33%
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32%
nonlinear problems
30%
anisotropy
29%
boundary conditions
28%
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26%
dirichlet problem
23%
vector fields
22%
volume
21%
stability
17%
range
17%
polynomials
16%
symmetry
16%
uncertainty principle
16%
one-dimensional calculations
15%
differential operators
13%
cauchy problem
13%
potentials
12%
green function
12%
weight
12%
cylinders
11%
comparative evaluations
11%
lyapunov method
10%
approximations
9%
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9%
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9%
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9%
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9%
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8%
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7%
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7%
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6%
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6%
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6%
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6%
metrics
6%
variational methods
5%
diffusion equations
5%
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5%
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5%
Mathematics
Type Inequality
76%
Laplace Operator
71%
Hardy Inequality
63%
Lie Group
54%
Eigenvalue
30%
Variable Coefficient
27%
Heisenberg Group
27%
Fractional Differential Equations
25%
Boundary Condition
21%
Isoperimetric Inequality
20%
Vector Field
19%
Circular Cylinder
15%
Differential Equation
14%
Boundary Value Problems
13%
Maximizer
13%
Integral Operator
13%
Rayleigh
12%
Polynomials Method
12%
Green Function
12%
Heat Equation
12%
Constant Coefficient
11%
Differential Operator
11%
Fractional Integral
11%
Remainder Term
10%
Boundedness
10%
Infinite Series
10%
Potential Theory
10%
Comparison Principle
9%
Nilpotent
9%
Half Space
9%
Euclidean Space
9%
Green's Identity
9%
Polynomial
9%
Leffler Function
9%
Abelian Case
9%
Initial-Boundary Value Problem
8%
Euler Operator
7%
Fundamental Solution
7%
Fractional Order
7%
Illustrative Example
7%
Necessary Condition
7%
Fractional Laplacian
7%
Explicit Solution
6%
Integro-Differential Operator
6%
Embedding Theorem
6%
Weak Solution
6%
Finite Time
6%
Wave Equation
6%
Lp Space
6%
Nonlinearities
6%
Keyphrases
Hardy Inequality
71%
Homogeneous Groups
46%
Stratified Group
28%
Rellich Inequality
24%
Heisenberg Group
21%
Stratified Lie Group
19%
Isoperimetric Inequality
17%
P-sub-Laplacian
17%
Homogeneous Lie Group
17%
Sub-Laplacian
15%
Fractional Differential Equations
13%
Differential Equations with Variable Coefficients
13%
Sharp Remainder
12%
Caffarelli-Kohn-Nirenberg Inequality
12%
Constant Coefficients
12%
Fractional Laplacian
11%
Volume Potential
11%
First Eigenvalue
10%
Potential Operator
10%
Heat Operator
10%
Poincaré Inequality
10%
Blow-up Result
10%
Sobolev Type Inequalities
10%
Geometric Hardy Inequality
10%
Riesz Potential
9%
Rellich
9%
Quasi-norm
9%
Infinite Series
9%
Lyapunov Inequality
9%
Green Identity
9%
Heat Polynomials Method
9%
Eigenvalues
8%
Dirichlet
8%
Uncertainty Principle
8%
Vector Field
8%
Time-fractional
7%
Cauchy Problem
7%
Initial-boundary Value Problem
7%
Simple Proof
7%
Nilpotent Lie Group
7%
Newtonian Potential
6%
S-numbers
6%
Fractional Derivative
6%
Best Constant
6%
Euclidean Space
6%
Sharp Constants
6%
Polyharmonic Equation
6%
Logarithmic Nonlinearity
6%
Rockland Operator
6%
Two-phase Inverse Stefan Problems
6%